Eighteen years ago, when Peter Gray was born, his father Dorian Gray opened a saving account as he wanted to make a gift of $150,000 to his son when the latter reaches the age of 18. To achieve this goal, Dorian Gray made equal deposits of $400 at the end of each month for 12 years, then the accumulated balance was left to grow for the remaining 6 years at 7% p.a.


(a) Determine the implied effective annual rate (EAR) on Dorian’s saving account over the first period of 12 years. Assume that there was monthly compounding for 12 years and annual compounding for the following 6 years.

My answer is: EAR = 8.90%

(b)On his 18th birthday, Peter receives his father’s gift money and decides to use it to pay for his college education. His degree in finance will require four years of study and is expected to cost $12,000 per semester. The payments need to be made semiannually at the beginning of each semester (the first payment is due now). The account will average 8% annually (APR quoted by the bank). What is the effective annual rate earned on the account for the period of four years (assume semiannual compounding)?
My answer is: 8.16%

(c) On his graduation day, Peter buys his dream car spending all the remaining balance on the account. What is the cost of the car?

my answer is $78000

(d) Show numerically that a saving account with a current balance of $1,000 that earns interest at 9% annually is precisely sufficient to make the payments on a three year loan of $1,000 which carries equal annual payments at 9% interest.

My answers is: Intrest paid$90 = Interest earnerd $90