# Annuities Calculator

 Present Value Accum Value Payment N Interest Rate Immediate Due

Given an interest rate of 10% and a payment amount of 5000 for 9 periods, calculate the Present Value (PV) and Accumulated Value (AV) of an Annuity Immediate:

The formula for the present value of an annuity immediate (PV) is denoted below:
 an|i = Payment * (1 - vn) i

Calculate v:
 v = 1 1 + i

 v = 1 1 + 0.1

 v = 1 1.1

v = 0.91

Calculate PV given i = 0.1, n = 9, and v = 0.91
 a9|0.1 = 5000 * (1 - 0.919) 0.1

 a9|0.1 = 5000 * (1 - 0.48) 0.1

 a9|0.1 = 5000 * 0.52 0.1

 a9|0.1 = 276 0.1

a9|0.1 = 28795.1191

The formula for the accumulated value of an annuity immediate (AV) is denoted below:
 sn|i = Payment * ((1 + i)n - 1) i

Calculate AV given i = 0.1, n = 9
 s9|0.1 = 5000 * ((1 + 0.1)9 - 1) 0.1

 s9|0.1 = 5000 * (1.19 - 1) 0.1

 s9|0.1 = 5000 * (2.357947691 - 1) 0.1

 s9|0.1 = 5000 * 1.357947691 0.1

 s9|0.1 = 6789.74 0.1

s9|0.1 = 67897.3846

How much of the accumulated value is principal and interest?:
Principal = Payment Amount * n
Principal = 5000 * 9
Principal = 45000

Calculate Interest Paid:
Interest Paid = Accumulated Value - Principal
Interest Paid = 67897.3846 - 45000
Interest Paid = 22897.38