Question

(d) Sam is planning to arrange a tailor-made bank deposit investment plan that can generate a regular annual interest income of $35,000, starting with the first payment received 6 years from now and the last payment received 15 years from now. Calculate the present value of this annuity amount at Year 3, given the relevant discount rate is 12% per annum. (e) If Sam is attracted by another investment compounded quarterly that grow 50% in 4 years, calculate the annual interest rate (APR) and effective annual rate (EAR) being earned for the investment. (1) Sam invests $200,000 at Bank A that earns an annual interest rate of 12% compounded monthly. His wife puts $220,000 at Bank B with an annual interest rate of 6% compounded monthly. How long does Sam take to accumulate his account at bank A to arrive a doubled accumulated amount of his wife's at bank B?

Answer 1

(d)

PV of Annuity(at Year 6) = P*[1-{(1+i)^-n}]/i

where, P = Annuity = 35000, i = Interest Rate = 0.12, n = Number of Periods = 6 to 15 years = 10

= 35000*[1-{(1+0.12)^-10}]/0.12

= 35000*0.678/0.12

= $197750

PV at Year 3 = PV at Year 6/[(1+Interest Rate)^Number of Years] = 197750/[(1+0.12)^3] = 197750/1.404928 = $140754.544

(e)

APR = Total Return in n years/n = Total Return in 4 years/4 = 50/4 = 12.5%

Effective Rate for 4 years = [{1+(Quarterly Rate)}^(Number of Quarters)]-1

0.5 = [{1+(QR)}^(16)]-1

1.5 = (1+QR)^16

Therefore, Quarterly Rate = (1.5^1/16) - 1 = 1.025665-1 = 0.025665 = 2.5665%(approx)

Annual Effective Rate(EPR) = [(1+Quarterly Rate)^4]-1 = [(1+0.025665)^4]-1 = 0.10668 = 10.668%(approx)

Cross Verification = 100*[(1+0.10668)^16] = 100*5.06 = 506(approx)

(f)

Therefore, It will take 159 months or 13 years and 3 months.