Question

1. How much money do you need to put away every year for the first 10 years into an account, that earns an interest rate of 2% compounded quarterly, if you expect to have $250,000 at the end of the 15^th year?
2. You now invest this $250,000 (lump sum) into another account for 15 more years. What is the interest rate, compounded annually, that you should look for if you need to have $325,000 at the end of the period?

Answer 1

(A)

Quarterly interest rate = 2%/4 = 0.5%

Number of quarters in 10 years = 10 x 4 = 40

Number of quarters in 5 years = 5 x 4 = 20

Value of $250,000 at end of year 10 (discounted by 5 years) ($) = 250,000 x P/F(0.5%, 20) = 250,000 x 0.9051 = 226,275

Required annual saving ($) = 250,000 / F/A(0.5%, 40) = 226,275 / 44.1588** = 5,124.12

(B) If required annual interest rate be R, then

$250,000 x (1 + R)¹⁵ = $325,000

(1 + R)¹⁵ = $325,000 / $250,000 = 1.3

Taking 15th root on each side,

1 + R = 1.0176

R = 0.0176

R = 1.76%

**P/F(0.5%, 20) = (1.005)^-20 = 0.9051

**F/A(0.5%, 40) = [(1.005)⁴⁰ - 1] / 0.005 = (1.2208 - 1) / 0.005 = 0.2208 / 0.005 = 44.1588