Question1 a At the beginning of each month an investor depos

Question1 a) At the beginning of each month an investor deposits $2,000 into an account that earns 3% annum compound interest. What is the value of the investment (present worth) at the end of 5 years? per b) A $2,000 000 mortgage has a 30-year repayment period and annum. What is the yearly installment and monthly installment? (5 marks) the compound-interest rate is 6% per (5 marks)

Solution

(a)

Monthly interest rate = 3%/12 = 0.25%

Number of months = 5 x 12 = 60

Present worth (PW) ($) = 2,000 x P/A(0.25%, 60) x 1.0025^# = 2,005 x 55.6524** = 111,582.98

#Since investment is at beginning of month, this is an annuity due and we need to use a multiplicative factor equal to (1 + Interest rate) = (1 + 0.0025) = 1.0025

**P/A(r%, N) = [1 - (1 + r)^-N] / r

P/A(0.25%, 60) = [1 - (1.0025)^-60] / 0.0025 = (1 - 0.8609) / 0.0025 = 0.1391 / 0.0025 = 55.6524

(b)

(1) Yearly installment = Loan amount / P/A(6%, 30) = $2,000,000 / 13.7648^# = $145,298.15

(2) Monthly interest rate = 6%/12 = 0.5% and number of months = 12 x 30 = 360

Monthly installment = Loan amount / P/A(0.5%, 360) = $2,000,000 / 166.7916** = $11,991.01

**P/A(r%, N) = [1 - (1 + r)^-N] / r

P/A(0.5%, 360) = [1 - (1.005)^-360] / 0.005 = (1 - 0.1660) / 0.005 = 0.8340 / 0.005 = 166.7916