Enter what you know below

<-- Present Val
<-- Accum Val
<-- Payment
<-- n
<-- Interest Rate
<-- Immediate
<-- Due
  
For an Annuity Immediate:
Payment = 1
n = 5
Interest Rate = 10
Calculate Present Value, Accumulated Value

PV annuity immediate formula:

an|i  =  Payment * (1 - vn)
  i

Calculate v:

v  =  1
  1 + i

v  =  1
  1 + 0.1

v  =  1
  1.1

v = 0.90909090909091

Calculate PV given i = 0.1, n = 5, and v = 0.90909090909091

a5|0.1  =  1 * (1 - 0.909090909090915)
  0.1

a5|0.1  =  1 * (1 - 0.62092132305916)
  0.1

a5|0.1  =  1 * 0.37907867694084
  0.1

a5|0.1  =  0.37907867694084
  0.1

a5|0.1 = 3.7908

AV annuity immediate formula:

sn|i  =  Payment * ((1 + i)n - 1)
  i

Calculate AV given i = 0.1, n = 5

s5|0.1  =  1 * ((1 + 0.1)5 - 1)
  0.1

s5|0.1  =  1 * (1.15 - 1)
  0.1

s5|0.1  =  1 * (1.61051 - 1)
  0.1

s5|0.1  =  1 * 0.61051
  0.1

s5|0.1  =  0.61051
  0.1

s5|0.1 = 6.1051

How much of AV is principal?:

Principal = Payment Amount * n
Principal = 1 * 5
Principal = 5

Calculate Interest Paid:

Interest Paid = Accumulated Value - Principal
Interest Paid = 6.1051 - 5