# Math 125 - Basic Calculus

```MATH 123, EXAM #3
Total Points: 100
3-5-2001
Report all dollar amounts to 2 decimal places, i.e., to the nearest cent. Report all rates as percentages to 2
decimal places, for example, report 0.0534 as 5.34%. Good luck.
1. (15 points) A loan of \$3,000 was repaid at the end of 11 months with a check for \$3,412.50. What
annual rate of interest was charged?
Simple Interest: I = 412.50, P = 3000, t = 11/12
(Use I = Prt)
r = .15 or 15.00%
2. (15 points) You have \$3,000 toward the purchase of a boat that will cost \$4,500. How long will it take
for the \$3,000 to grow to \$4,500 if it is invested at 8% compounded quarterly?
Compound Interest: A = P(1+i)n
4500 = 3000(1.02)n solve for n
1.5 = 1.02n
take log of both sides
n  20.5
So, it will take 21 quarters or 5 years and 3 months.
3. (15 points) What is the value of an ordinary annuity at the end of 9 years if \$300 per month is deposited
into an account earning 6% compounded monthly?
FV of annuity: FV = 300[1.005108 – 1]/.005 = \$42,821.97
4. (20 points) A company establishes a sinking fund for plant retooling in 6 years at an estimated cost of
\$850,000. How much should be invested semi-annually into an account paying 9% compounded semiannually? How much interest will the account earn during the 6 years?
FV of annuity: 850000 = PMT[1.04512 – 1]/.045
Interest = \$850,000 – 12(54,966.26) = \$190,404.88
PMT = \$54,966.26
5. (15 points) A rich uncle wills you an annuity paying \$5,000 per quarter for the next 12 years. If the
money is worth 10% compounded quarterly, what is the present value of this annuity?
PV of annuity: PV = 5000[1 – 1.025 –48]/.025 = \$138,865.77
6. (20 points) A law firm buys a computerized word-processor system costing \$12,000. If they pay 25%
down and amortize the rest with equal monthly payments over 6 years at 12% compounded monthly, what
will be the monthly payment? How much (total) interest will the firm pay?
PV of annuity: 9000 = PMT[1 – 1.01 –72]/.01
PMT = \$175.95
Interest = 72(\$175.95) – 9000 = \$3,668.52 (No interest paid on down payment)
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