accumulated value - The total value of an investment, including principal and interest accrued

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a func

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970
The formula for accumulated value of something with a percentage growth p and years x is:
V(x) = Initial Value * (1 + p/100)^x
Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have:
V(x) = 100 * (1 + 8/100)^50
V(x) = 100 * (1.08)^50
V(x) = 100 * 46.9016125132
V(x) = [B]4690.16[/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]

Annuities

Solves for Present Value, Accumulated Value (Future Value or Savings), Payment, or N of an Annuity Immediate or Annuity Due.

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]

Arithmetic Annuity

Calculates the Present Value, Accumulated Value (Future Value), First Payment, or Arithmetic Progression of an Increasing or Decreasing Arithmetic Annuity Immediate.

Continuous Annuity

Determines the Present Value and Accumulated Value of a Continuous Annuity

Geometric Annuity Immediate

Given an immediate annuity with a geometric progression, this solves for the following items

1) Present Value

2) Accumulated Value (Future Value)

3) Payment

1) Present Value

2) Accumulated Value (Future Value)

3) Payment

How much money must be invested to accumulate $10,000 in 8 years at 6% compounded annually?

How much money must be invested to accumulate $10,000 in 8 years at 6% compounded annually?
We want to know the principle P, that accumulated to $10,000 in 8 years compounding at 6% annually.
[URL='https://www.mathcelebrity.com/simpint.php?av=10000&p=&int=6&t=8&pl=Compound+Interest']We plug in our values for the compound interest equation[/URL] and we get:
[B]$6,274.12[/B]

Simple and Compound and Continuous Interest

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

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

You buy a house for $130,000. It appreciates 6% per year. How much is it worth in 10 years

You buy a house for $130,000. It appreciates 6% per year. How much is it worth in 10 years
The accumulated value in n years for the house is:
A(n) = 130,000(1.06)^n
We want A(10)
A(10) = 130,000(1.06)^10
A(10) =130,000*1.79084769654
A(10) = [B]232,810.20[/B]

You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a functio

You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a function that represents the balance after 4 years.
The Accumulated Value (A) of a Balance B, with an interest rate per compounding period (i) for n periods is:
A = B(1 + i)^n
[U]Givens[/U]
[LIST]
[*]4 years of quarters = 4 * 4 = 16 quarters. So this is t.
[*]Interest per quarter = 5/4 = 1.25%
[*]Initial Balance (B) = 750.
[/LIST]
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=750&nval=16&int=5&pl=Quarterly']compound balance interest calculator[/URL], we get the accumulated value A:
[B]$914.92[/B]