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MATH 253 THEORY OF INTEREST

Sample Midterm

Name: ______ID Number:______

Instructions:

Time allotted is 70 minutes. Books and notes may NOT be used.

Show all of your work.

QUESTION / VALUE / MARK
1 / 2
2 / 3
3 / 4
4 / 4
5 / 4
6 / 4
7 / 4
TOTAL / 25

Note: Calculations shown are abbreviated. Students are expected to show all their work and a neatly drawn time diagram where appropriate.
1.Find the nominal rate of discount convertible quarterly which is equivalent to an annual effective rate of interest of 10.5%

2. Calculate the present value today of $100000 10 years from now using

a)

b)simple interest of 9% per annum.

c)

a)

b)

c)

3. a) If where each payment is $1, calculate the effective annual interest rate using linear interpolation with interest rates that are 1% apart.

b)Using the answer in a) as a starting point, calculate the actual rate to 4 decimal places of accuracy using the iteration method of your choice.

a)

b)

i.e. actual interest is > .0424 and <.04244, so will round down to .0424

Answer is 4.24%

4. Frank just turned 70. At the age of 35, he began to put $6000 into an RRSP every year on his birthday. At age 45, he increased the yearly payment to 7500, and continued to make payments up to and including age 64. If the interest rate was 10% compounded annually for the first 10 years and 8% compounded annually thereafter, how much does Frank have at age 70?

5. Brad wants to purchase a perpetuity which will pay $2500 every quarter with payments starting in exactly 12 years. Calculate the single premium required today to purchase this perpetuity if

m=2r=4

6. Jim hopes to accumulate $225000 by January 1, 2010. He started making annual deposits of $5000 each on January 1, 1995, but he was unable to make the deposits in the years 2000, and 2001. On January 1, 2002 he plans to start making deposits again up to and including January 1, 2010. If he can earn 12% convertible quarterly on his deposits, past and future, calculate the level amount he must deposit on each January 1 from 2002 to 2010 in order to reach his target.

7. a)Frank buys a house for $210000. After putting a down payment of $25000, he gets a mortgage at a rate of 7.5% convertible semi-annually for the remaining amount. If he plans to pay $1475 towards the mortgage at the end of each month, calculate the number of payments he must make.

b) Calculate the amount of the final (drop) payment.

a)

Using logs, n=240.8987

b)