Question

You want to retire at age 65. You decide to make a deposit to yourself at the end of each year into an account paying 2%, compounded annually. Assuming you are now 25 and can spare $1,500 per year, how much will you have when you retire at age 65? (Round your answer to the nearest cent.) 5

Answer 1

The stream of payments each year is an annuity of $1,500 paid each year for ( 65- 25) = 40 years at 2% per annum

So, Future value of annuity

= P x [ ( 1 + r) ^ n – 1] / r

Where,

P = Periodic Payments = $1,500

r = Rate of interest = 2% or 0.02

n = Number of years = 40

So, Future Value

= $1,500 x [ ( 1.02 ^ 40 – 1)] / 0.02

= $1,500 x [1.208040 / 0.02]

= $1,500 x 60.402

= $90,603