Question

Derek can deposit $283.00 per month for the next 10 years into an account at Bank A. The first deposit will be made next month. Bank A pays 15.00% and compounds interest monthly. Derek can deposit $2,468.00 per year for the next 10 years into an account at Bank B. The first deposit will be made next year. Bank B compounds interest annually. What rate must Bank B pay for Derek to have the same amount in both accounts after 10 years?  Please use a financial calculator and show steps please

Answer 1

One payment is done monthly whereas the other is done annually. The monthly payment receives an interest that is compounded monthly whereas the annual payment is compounded annually. The case also says that the future value of both the payments should be equal.

Calculating the FV of the monthly payment that has an interest rate of 15% pa compounded monthly for the next ten years:

FV = 283*(1+0.15/12) + 283*(1+0.15/12)^2 + 283*(1+0.15/12)^3 + --------------------------- + 283*(1+0.15/12)^119 + 283*(1+0.15/12)^120

Using the GP formula,

FV = 283{(1+0.15/12)^120 - 1}/(0.15/12)

FV = 77886.4275

In financial calcullator use future value formula with, installment value = 2280, interest rate = 0.15/12 and period of payments = 120

Now we have to find the rate of interest for annual payment that could match the FV of the monthly payment,

FV = 2468*(1+r) + 2468*(1+r)^2 + 2468*(1+r)^3 + ------------------ + 2468*(1+r)^10

Using the GP formula,

FV = 2468{(1+r)^12 - 1}/r  

77886.4275 = 2468{(1+r)^12 - 1}/r  

Solving for r we get, r = 23.946 or 24% per annum