Question

1. Calculate the future value of $1,250, 7- year annuity invested at 9% APR.

(b) What would be the future value of an equivalent annuity due payments?

(c) Calculate the present value of $1,750, 5- year annuity using a discount rate of 12% APR.

(d) What would be the present value of an equivalent annuity due payments?

Answer 1

Part A and B

Future value of annuity is calculated based on the following formula :

Here rate = 9%, n = 7 years and P = $1,250

Putting values in to the formula :

FV of annuity = $1,250 * [{(1+9%)^7 - 1}/9%]

FV of annuity = $1,250 * 9.20

FV = $11,500.54

If the same annuity is annuity due, the whole amount will remain invested for one more year, thus we will multiply the annuity above by (1+rate) to arrive at annuity due value.

FV of annuity due = $11,500.54 * (1+9%) = $12,535.59

Part C and D

PV of annuity is calculated using the following formula :

Taking C = $1,250 , n = 5 years and rate = 12%

Putting value in to the formula :

PV = $1,250 * [{1-(1+12%)^-5} / 12%]

PV = 1,250 * 3.60

PV = $4,505.97

If the same annuity is annuity due, the whole amount will be discounted for one less year, thus we will multiply the annuity above by (1+rate) to arrive at annuity due value.

PV = $4,505.97 * (1+12%) = $5,046.69