Question

An investment of $31 700 is accumulated at 4.24% compounded quarterly for three and one-half years. At that time the interest rate is changed to 6.12% compounded monthly. How much is the investment worth two years after the change in interest rate?

Answer 1

Given that,

Initial investment PV = $31700

interest rate for 1st t = 3.5 years r = 4.24% compounded quarterly

So, accumulated value of the fund at the year 3.5 using compounding is

Accumulated value = PV*(1 + r/n)^(n*t)

For quarterly compounding, n = 4

=> Accumulated value at year 3.5 = 31700*(1+0.0424/4)^(4*3.5) = $36742.56

then interest rate changed to 6.12% compounded monthly

So, future value after 2 years is

FV = Accumulated value at 3.5 year*(1+r/n)^(n*t)

for monthly compounding n = 12

=> Future value FV = 36742.56*(1+0.0612/12)^(12*2) = $41513.75

So, Investment is worth $41513.75