UNIVERSITY OF GHANA
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EXERCISE 2: 2020/2021
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
ACTU 203: INTRODUCTION TO FINANCIAL MATHEMATICS 1 (3 credits)
1. Find the accumulated value of an ordinary simple annuity of GH¢2,000 per year for 5
years if money is worth
a. j1 = 9% compounded annually
b. j1 = 12 12 % compounded annually
2. Find the present value of an ordinary of GH¢380 at the end of each month for 3 years at
a. j12 = 12%
b. j12 = 10.38%
3. Charles buys a used car by paying GH¢1500 down and GH¢182.50 a month for 3 years.
a. what was the cash price of the car, if the interest rate on the loan is j12 = 18%?
b. what was the total interest on the loan?
4. Prove and interpret (1 + i)a n i = a n−1 i + 1
5. Jackie deposits GH¢200 at the beginning of each month for 5 years in an account paying
interest at 10 21 % compounded monthly. How much is in her account at the end of 5
years?
Dr Perpetual A. Boiquaye/ Dr Winnie Onsongo
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6. A couple wants to accumulate GH¢10,000 by December 31, 1999. They make 10 equal
annual deposits starting January 1, 1990. If interest is at j1 = 12% , what annual deposit
is needed?
7. A fund of GH¢8000 is to be accumulated by semiannual payments of GH¢200. If the fund
earns interest at j2 = 12%, find the number of full deposits required and the final deposit.
8. Find the interest rate, j2 , at which semiannual deposits of GH¢500 will accumulate to
GH¢6000 in 5 years.
9. A dealer sells an article for GH¢600. He will allow you to buy it for GH¢240 down, with
the balance to be paid in GH¢30 monthly installments for a year. If you pay cash, he will
give you a 10% discount.
a. what is the interest rate j12 paid by the purchaser who uses the installments plan?
b. what is the annual effective rate being charged on the installment plan?
Dr Perpetual A. Boiquaye/ Dr Winnie Onsongo
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