MATH400(Theory of Interest) Exam #2ReviewQuestions
The actual exam will consist of the questions here except that the portions in red will be different.
1.A family wants to accumulate $50,000 in a college education fund at the end of 25 years. They plan to deposit $1000 in the fund at the end of each of the first 10 years and $1000 + X in the fund at the end of each of the last15 years. If the fund earns 8% effective, find X.
2.Thecash price of an automobile is $30,000. The buyer is willing to finance the purchase at 15% convertible monthly and to make payments of $500 at the end of each month for five years. Find the down payment that will be necessary.
3.Aman borrows $30,000 for 10 years and repays the loan with level annual payments at the end of each year. If the loan carries an effective interest rate of 7.5%, find the amount of interest will he pay over the life of the loan.
4.Anannuity provides a payment of n at the end of each year for3 years. The effective annual interest rate is 1/n. Find the present value of the annuity.
5.A worker aged 40 wishes to accumulate a retirement fund by depositing $3000 at the beginning of each year for 15 years. Starting at age 55, the worker plans to make 25 equal annual withdrawals at the beginning of each year, with nothing left in the fund immediately after the last withdrawal. Find the amount of each withdrawal if the effective rate of interest is 10% during the first 15 years but only 8% thereafter.
6.Findthe present value on January 1 of an annuity which pays $800 every three months for four years, where the first payment is onFebruary 1. The rate of interest is 7% convertible semi-annually.
7.Adeferred perpetuity-immediate begins payment at time n with annual payments of $100,000 per year. If the present value of the perpetuity due is $531,441 and the effective rate of interest is i = 1/9, find n.
8.Payments of $100 a year are made into a 12year annuity immediate. The effective rate of interest is 4% for the first eight years and 6% for the last four years. Find the accumulated value of the annuity at the end of the 12year period.
9.A loan of $10,000 is to be repaid in annual payments of $1000which begin at the end of the eighth year and continue thereafter for as long as necessary. With an annual effective interest rateof6.5%, find each of the following:
(a) the time for, and the amount of, the smaller additional payment according to the “mathematical” model,
(b) the balloon payment which is smaller than each regular payment and is added tothe last regular payment,
(c) the drop payment which is smaller than each regular payment and is made one month after the last regular payment.
10.Theaccumulation function for a certain 5year investment is
a(t)= .
(a)Find the effective interest rate for year n.
(b)Find the accumulated value after four years when deposits of $800 are made at the beginning of each of the three years.
(c)Find the present value of deposits of $1000 made at the end of each of the next four years.
11.Find the accumulated value 21 years after the first payment is made into an annuity on which there are 10 payments of $3000 each made at three-year intervals. The nominal rate of interest is 7% convertible semi-annually.
12.Find the present value of an annuity that pays $200 at the beginning of each halfyear for 10 years. The interest rate is 9% compounded three times a year.
13.The there is $60,000 in a fund which is accumulating at 6% per annum convertible continuously, and today we begin withdrawing the money continuously at the rate of $3600 per annum. Find how long the fund will last.
14.Aperpetuity-due has annual payments of 3, 6, 9, 12, 15, 18, …. If the interest is 8% effective, find the present value of the perpetuity.
15.Annualdeposits are made into a fund at the beginning of each year for 12 years. The first 7 deposits are $600 each and the deposits increase by 2.5% per year thereafter. If the fund earns 5% effective, find the accumulated value at the end of the 12 years.
16.Suppose interest if 7% effective, and the payments for a perpetuityare 1 at the end of each of the 1st, 2nd, and 3rd years, 2 at the end of each of the 4th, 5th, and 6th years, 3 at the end of each of the 7th 8th, and 9th years, etc. find the present value of the perpetuity.
17.Aman endows an annuity, the present value of which is to be split equally between charities A and B. At the end of each year, charity A will receive a fixed amount for 30 years. And then, beginning at the end of year 31, charity B will receive $500 at the end of each year in perpetuity. Find the present value of the annuity.
18.Anannuity will begin quarterly payments in 3 months and continue untila total of 24 payments are made. The first payment will be $3000, and each payment will be $300 less than the previous payment. Find the present value of the annuity.
Answers to MATH 400(Theory of Interest) Exam #2 ReviewQuestions
1.X = $9918.85
2.$8982.70
3.t = 17.667 years
4.