Question

In 4 years, you will start receiving monthly payments of $1000 from a trust fund that one of your great parents set up for you. The first payment will be made at the very end of year 4 and the payments will last for 33 years. You plan to deposit the money you receive every month into a special account right away that pays 6.80% APR with quarterly compounding.

Today the account mentioned above has a balance of $13000.

Assuming that interest rate will stay constant, what will be the account balance at the end of the 12th year?

Answer 1

Effective Interest Rate or EAR = [{1+(APR/n)}^n]-1

Where, APR = Annual Interest Rate or Nominal Rate, n = Number of times compounded in a year

For Quarterly,

EAR = [{1+(0.068/4)}^4]-1 = 0.06975

FV of 13000 after 12 years = PV*[(1+EAR)^12] = 13000*[(1+0.06975)^12] = 29197.73

FV of 1000 per annum for 8 years = P*[{(1+i)^n}-1]/i

Where, P = Annuity = 1000, i = Interest Rate = 0.06975, n = Number of Periods = 8

Therefore, FV = 1000*[{(1+0.06975)^8}-1]/0.06975 = 1000*0.715025/0.06975 = 10250.71

Account Balance after 12 years = FV of 13000+FV of 1000 for 8 years = 29197.73+10250.71 = $39448.44