Question

3.

a)

You plan to save money for a down payment of $42,000 to purchase an apartment. You can only afford to save $1,250 at the end of every quarter int an account that earns interest at 4.50% compounded annually. How long wil it take you to save the planned amount? months O years Express the answer in years and months, rounded to the next payment period

b)

Answer 1

(a) Target Future Value = $ 42000, Periodic (quarterly) Payment = $ 1250, Annual Interest Rate = 4.5 %, Compounded Frequency: Annual

Equivalent Quarterly Rate = [(1.045)^(1/4)-1] = 0.011065 or 1.1065 %

Let the number of quarters required to reach the target future value be N

Therefore, 1250 x (1.011065)^(N-1) + 1250 x (1.011065)^(N-2) +................+ 1250 = 42000

1250 x [{(1.011065)^(N) - 1}/{(1.011065)-1}] = 42000

(1.011065)^(N) = 1.371784

N = = 28.7265 quarters or 86.18 months ~ 7 years and 2 months

lo91.011065 1.371784

(b) Cost of Truck = $ 54000, Down Payment = $ 4860, Monthly Repayments = $ 1900, Compounding Frequency: Semi-Annual, Annual Interest Rate = 5.7%

Borrowing = 54000 - 4860 = $ 49140

Applicable Semi-Annual Rate = 5.7 / 2 = 2.85 %

Equivalent Monthly Rate = (1.0285)^(1/6) - 1 = 0.00469 or 0.469 %

Let the number of months required to pay off the loan be N months

Therefore, 49140 = 1900 x (1/0.00469) x [1-{1/(1.00469)^(N)}]

49140 = 404724.0456 x [1-{1/(1.00469)^(N)}]

0.121416 = [1-{1/(1.00469)^(N)}]

1/(1.00469)^(N) = 1 - 0.121416 = 0.878584

(1.00469)^(N) = 1/0.878584 = 1.138195

N = = 27.6378 months ~ 28 months or 2 years and 4 months

lo91.00469 1.138195