Question

QUESTION11

a. The required return is 4.1​% APY​ (EAR). Suppose you borrow ​$27574 for college expenses today. What will be your payments per month if you will repay the loan over a period of  63 ​months, with your first payment being made 30 months from​ today? ​ (Rounded to the nearest​ cent.)

b. The required return is 9.9​% APY​ (EAR). How much would you need to save per month for the next 46 years so that you will have ​$0.925 million saved to retire​ on, 46 years from​ now, assuming your first payment is made one month from​ today? ​ (Rounded to the nearest 10​ cents.)

Answer 1

(a) EAR = 4.1%, Borrowings = $ 27574, Repayment Tenure = Month 30 to Month 63 (both included), Total Number of Repayments = (63-30) + 1 = 34

Applicable Monthly Interest Rate = (1.041)^(1/12) - 1 = 0.0033541 or 0.33541 %

Let the monthly repayments be $ m

Therefore, 27574 = m x (1/0.0033541) x [1-{1/(1.0033541)^(34)}] x [1/(1.0033541)^(29)] = m x 29.1133

m = 27574 / 29.1133 = $ 947.12677 ~ $ 947.13

(b) EAR = 9.9 %, Applicable Monthly Rate = (1.099)^(1/12) - 1 = 0.00789775 or 0.789775 %

Target Future Value = $ 0.925 million or 925000 and Deposit Tenure = 46 years or (46 x 12) = 552 months

Let the end of month deposits be $ p

Therefore, p x (1.00789775)^(551) + p x (1.00789775)^(550) + p x (1.00789775)^(549) +...................+ p = 0.925

p x [{(1.00789775)^(552) - 1} / {1.00789775 - 1}] = 0.925

p x 9609.607443 = 0.925

p = 925000 / 9609.607443 = $ 96.2578 ~ $ 96.26