26 results

principal - The amount borrowed on a loan, before interest is charged

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, w

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, written as a decimal (1%=.01, 2%=.02,etc) , n=number of times per year, t= number of years
So we have:
[LIST]
[*]$300 principal
[*]13 * 2 = 26 periods for n
[*]Rate r for a semiannual compound is 8%/2 = 4% per 6 month period
[/LIST]
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=300&int=4&t=26&pl=Compound+Interest']compound interest with balance calculator[/URL], we get:
[B]$831.74[/B]

A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number

A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number of T-shirts for the school store. The total cost of the order was $1,520. Which equation can be used to find the number one f shirts ordered?
Set up the cost equation C(f) where f is the number of shirts:
C(f) = Cost per shirt * f + Shipping
We're given C(f) = 1520, Shipping = 22, and cost per shirt is 7, so we have:
[B]7f + 22 = 1520
[/B]
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=7f%2B22%3D1520&pl=Solve']type this equation in our search engine[/URL] and we get:
f = [B]214[/B]

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuousl

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuously. Using the formula V = Pe^{rt}V=Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=230&int=6.8&t=20&pl=Continuous+Interest']continuous compounding calculator[/URL], we get:
V = [B]896.12[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuou

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get:
V = 96,300 * e^(0.028 * 7)
V = 96,300 * e^0.196
V = 96,300 * 1.21652690533
V = [B]$117,151.54[/B]

A principal of $2200 is invested at 6% interest, compounded annually.How much will investment be wor

A principal of $2200 is invested at 6% interest, compounded annually.How much will investment be worth after 10 years?
Use our [URL='http://www.mathcelebrity.com/compoundint.php?bal=2200&nval=10&int=6&pl=Annually']balance calculator,[/URL] we get:
[B]$3,939.86[/B]

A principal of $3300 is invested at 3.25% interest, compounded annually. How much will the investmen

A principal of $3300 is invested at 3.25% interest, compounded annually. How much will the investment be worth after 10 years?
[URL='https://www.mathcelebrity.com/compoundint.php?bal=3300&nval=10&int=3.25&pl=Annually']Using our balance calculator with compound interest[/URL], we get:
[B]$4,543.75[/B]

Amy deposits 4000 into an account that pays simple interest at a rate of 6% per year. How much inter

Amy deposits 4000 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 4 years?
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=4000&int=6&t=4&pl=Simple+Interest']simple interest calculator[/URL], we get an accumulated value of 4,960
Interest Paid = Accumulated Value - Principal
Interest Paid = 4960 - 4000
Interest Paid = [B]960[/B]

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how m

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how much is in the account after 7 years? How much of this is interest?
Let's assume payments are made at the end of each month, since the problem does not state it. We have an annuity immediate formula. Interest rate per month is 6.6%/12 = .55%, or 0.0055. 7 years * 12 months per year gives us 84 deposits.
Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=950&n=84&i=0.55&check1=1&pl=Calculate']present value of an annuity immediate calculator[/URL], we get the following:
[LIST=1]
[*]Accumulated Value After 7 years = [B]$101,086.45[/B]
[*]Principal = 79,800
[*]Interest Paid = (1) - (2) = 101,086.45 - 79,800 = [B]$21,286.45[/B]
[/LIST]

Calculate the simple interest if the principal is 1500 at a rate of 7% for 3 years

Calculate the simple interest if the principal is 1500 at a rate of 7% for 3 years.
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=1500&int=7&t=3&pl=Simple+Interest']simple interest calculator[/URL], the total interest earned over 3 years is [B]$315[/B].

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time pe

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.
Our givens are:
[LIST]
[*]I = 450
[*]P = 3000
[*]t = 3
[*]We want r
[/LIST]
450 = 3000(r)(3)
450 = 9000r
Divide each side by 9000
[B]r = 0.05[/B]

Find the elements on the principal diagonal of matrix B

Find the elements on the principal diagonal of matrix B
Matrix B:
|0 0 8|
|-1 3 0|
|2 -5 -7|
The main diagonal is any entry where row equals column
|[B]0[/B] 0 8|
|-1 [B]3 [/B] 0|
|2 -5 [B]-7[/B]|
In this case, it is [B]0, 3, -7[/B]

I invest $3000 at 5% interest a year. So far I have made $600 with simple interest. How many years h

I invest $3000 at 5% interest a year. So far I have made $600 with simple interest. How many years have I been investing?
Simple interest is calculated using interest * principal.
We have 5% * 3000 = $150 interest per year
We take our $600 of total interest and divide it by our interest per year to get the total years:
$600 / $150 = [B]4 years[/B]

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula to compute a mortgage payment, M, is shown below, where P is the principal amount of the loan, r is the monthly interest rate, and N is the number of monthly payments. Janice's bank offers a monthly interest rate of 0.325% for a 12-year mortgage. How many monthly payments must Janice make?
12 years * 12 months per year = [B]144 mortgage payments[/B]

John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on

John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on the other. How much did he invest in each if the total amount earned was 880?
The first principal portion is x. Which means the second principal portion is 20,000 - x. We have:
0.04x + 0.05(20,000 - x) = 880
0.04x + 1,000 - 0.05x = 880
Group like terms:
-0.01x + 1000 = 880
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=-0.01x%2B1000%3D880&pl=Solve']equation solver[/URL], we get x = [B]12,000[/B]. Which means the other fund has 20,000 - 12,000 = [B]8,000[/B].

Match each variable with a variable by placing the correct letter on each line.

Match each variable with a variable by placing the correct letter on each line.
a) principal
b) interest
c) interest rate
d) term/time
2 years
1.5%
$995
$29.85
[B]Principal is $995
Interest is $29.85 since 995 * .0.15 * 2 = 29.85
Interest rate is 1.5%
Term/time is 2 year[/B]s

Mortgage

Free Mortgage Calculator - Calculates the monthly payment, APY%, total value of payments, principal/interest/balance at a given time as well as an amortization table on a __standard__ or __interest only__ home or car loan with fixed interest rate. Handles amortized loans.

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded contin

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (?2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent.
[URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=3&t=14&pl=Continuous+Interest']Using our continuous interest calculator[/URL], we get:
A = [B]1,521.96[/B]

principal $3000, actual interest rate 5.6%, time 3 years. what is the balance after 3 years

principal $3000, actual interest rate 5.6%, time 3 years. what is the balance after 3 years
[URL='https://www.mathcelebrity.com/compoundint.php?bal=3000&nval=3&int=5.6&pl=Annually']Using our compound interest calculator[/URL], we get a final balance of:
[B]$3,532.75[/B]

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much inte

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 years?
The formula for [U]interest[/U] using simple interest is:
I = Prt where P = Principal, r = interest, and t = time.
We're given P = 500, r =0.04, and t = 4. So we plug this in and get:
I = 500(0.04)(4)
I = [B]80[/B]

Reece made a deposite into an account that earns 8% simple interest. After 8 years reece has earned

Reece made a deposite into an account that earns 8% simple interest. After 8 years Reece has earned 400 dollars. How much was Reece's initial deposit?
Simple interest formula:
A = P(1 + it) where P is the amount of principal to be invested, i is the interest rate, t is the time, and A is the amount accumulated with interest.
Plugging in our numbers, we get:
400 = P(1 + 0.08(8))
400 = P(1 + 0.64)
400 = 1.64P
1.64P = 400
[URL='https://www.mathcelebrity.com/1unk.php?num=1.64p%3D400&pl=Solve']Typing this problem into our search engine[/URL], we get:
P = [B]$243.90[/B]

Simple and Compound and Continuous Interest

Free Simple and Compound and Continuous Interest Calculator - Calculates any of the four parameters of the simple interest formula or compound interest formula or continuous compound formula

1) Principal

2) Accumulated Value (Future Value)

3) Interest

4) Time.

1) Principal

2) Accumulated Value (Future Value)

3) Interest

4) Time.

Simple Discount and Compound Discount

Free Simple Discount and Compound Discount Calculator - Given a principal value, interest rate, and time, this calculates the Accumulated Value using Simple Discount and Compound Discount

Six is the principal square root of 36

Six is the principal square root of 36
The two square roots of 36 are:
[LIST]
[*]+6
[*]-6
[/LIST]
The positive square root is known as the principal square root, therefore, this is [B]true[/B].

Split Fund Interest

Free Split Fund Interest Calculator - Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.

The principal randomly selected six students to take an aptitude test. Their scores were: 87.4 86.9

The principal randomly selected six students to take an aptitude test.
Their scores were: 87.4 86.9 89.9 78.3 75.1 70.6
Determine a 90% confidence interval for the mean score for all students.

You put $5500 in a bond fund which has an annual yield of 4.8%. How much interest will be earned in

You put $5500 in a bond fund which has an annual yield of 4.8%. How much interest will be earned in 23 years?
Build the accumulation of principal. We multiply 5,500 times 1.048 raised to the 23rd power.
Future Value = 5,500 (1.048)^23
Future Value =5,500(2.93974392046)
Future Value = 16,168.59
The question asks for interest earned, so we find this below:
Interest Earned = Future Value - Principal
Interest Earned = 16,168.59 - 5,500
Interest Earned = [B]10,668.59[/B]