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46 h h , < " W W W W W ! ! ! ! ! ! ! $ # b& F ! H ! W W ! n n n R W W ! n ! n n V @ W 0 p C s! ! 0 " O x & X & & n ! ! n " & : ENM 530 Practice Quiz 1
1. You borrowed $2,000 from your parents and promised to pay them $2,500 after 3 years. The simple interest rate that you have in mind is closest to
a) 8.3% b) 8.5% c) 9.3% d) 8% e) not given
I = 500 = 2000 * i * 3 => i = 8.33%
2. The effective interest rate of 6% interest rate compounded quarterly is:
a) 6.09% b) 6.14% c) 6.34% d) 6.32%.
Effective interest rate, ia = (1 + 0.06/4)4 - 1 = 0.06136 or 6.14% .
3. An individual wishes to deposit an amount of money now and $100 every six months so that at the end of five years $1,500 will have been accumulated. With interest at 4% per year, compounded semiannually, how much should be deposited now?
a) $455.35 b) $510.95 c) $332.24 d) $284.51
F = $1,500 Number of semi-annual periods for 5 years = 10 Interest rate/period = 4/2 = 2%
1,500 = P (F/P, 2%, 10) + 100(F/A, 2%, 10)
1,500 = P (1.219) +100 (10.950) P = (1,500 - 1,095)/1.219 = $332.24
4. A payday loan business in town charges $3 interest per two week on a $200 loan. The effective interest rate on this loan is ______.
a) 39% b) 47.27% c) 52.1% d) None of these
Effective interest rate = (1+ 3/200)26 - 1 = 0.4727 or 47.27%
Data for next 5 problems
A debt of $10,000 must be paid in a series of equal monthly payments for 5 years. The nominal annual interest rate is 12%, compounded monthly.
5. The amount of each payment is equal to _______________.
a) $166.67 b) $185.33 c) $222.00 d) $192.91
A = 10,000(A/P, 1%, 60) = 10,000(0.0222) = $222
6. The effective interest rate for this loan is ______________.
a) 12% b) 13.12% c) 12.68% d) none of these
ieff = (1 +0.01)12 - 1 = 0.1268 = 12.68%
7. The loan balance immediately after the 12th payment is ______________.
a) $8,000 b) $8,430 c) $7,298 d) None of these
Loan balance immediately after the 12th payment = 222(P/A,1%,48) = 222(37.974) = $8,430
8. The total interest paid on this debt is _________________.
a) $2,000 b) $2,712 c) 1, 500 d) $3,320
Total interest payments = 60(222) -10,000 = $3,320
9. The quarterly payment, if interest is compounded quarterly, is _____________.
a) $598 b) $766 c) $672 d) $499
Interest rate, i /quarter = 12%/4 = 3% Number of quarterly periods = 5(4) = 20
A = 10,000 (A/P, 3%, 20) = 10,000(0.0672) = $672
10. One hundred dollars of interest is paid each month on an investment of $10,000. If interest is compounded monthly, the accumulation at the end of two years is equal to ____________.
a) $12,400 b) $12,700 c) $12,544 d) $12,400
Interest rate per monthly period = 100/10,000 = 0.01 or 1%
Number of monthly periods for 2 years, n = 24
F = $10,000(F/P, 1%, 24) = 10,000(1.270) = $12,700
11. A sum of $5,000 is invested for five years with varying annual interest rates of 9%, 8%, 12%, 6%, and 15%, respectively. The future amount after 5 years is equal to ____________.
a) $8,052.55 b) $7,693.12 c) $8,036.04 d) $7,907.20
F = 5,000 (F/P, 9%, 1) (F/P, 8%, 1) (F/P, 12%, 1) (F/P, 6%, 1) (F/P, 15%, 1)
F = 5,000 (1.09) (1.08) (1.12) (1.06) (1.15) = $ 8,036.04
12. An individual wishes to deposit an amount of money now to have an accumulation of $500 at the end of five years. If the interest rate is at 4% per year, compounded semiannually, how much should be deposited now?
a) $337.80 b) $740.00 c) $410.15 d) $454.54
F = $500 Number of interest periods = 10 (semi-annual periods) i = 2%/period
P = F (P/F, i, n) = 500 (P/F, 2%, 10) = 500(0.8203) = $410.15.
13. A sum of $1,000 deposited at time 0 at an interest rate of 5% compounded quarterly for 5 years. The future worth of this deposit is equal to ____________.
a) $1,314 b) $1,307 c) $1,307 d) $1,252.50
F = $1,000(1 + 0.055/4)20 = $1,314
14. Given a cash flow table below, compute the present worth for an interest rate of 10%
n 1 2 3 4 5 6 7
cf 3K 3K 3K -5K 3K 3K 3K
P = 3K(P/A, 10%, 7) 8K(P/F, 10%, 4)
= 3K(4.868) 8K(0.6830)
= $ 9,140
15. The value of X for the 2 equivalent cash flows shown below at 15% compounded annually is
n 0 1 2 3 4 5 A -1000 X 1.5X 2X 2.5X 3X B -2500 3000 2500 2000 1500 1000
a) $908.52 b) 1109.67 c) 850.67 d) 1043.89
15. Find the exact interest rate of return for the following cash flow.
n 0 1 2 3 cf -1K 300 200 800
16. A firm has zero revenues at year 1 but the revenues grow $15K per year over the next 5 years. At 10% Annual interest, the present worth is closest to
$75K b) $103K c) $33.3K d) $145.3K
(cubic -10 3 2 8) ( 1.118404 => i = 11.84%
(list-pgr '(-1000 300 200 800) 11.84) ( 7.263184e-3 ( 0
17. Are the cash flow diagrams equivalent t at 14% per year?
$10M $48M
1 2 3 4 5 1 2 3 4 5
18. 100 shares were bought at end of year 2004 for $20 each and sold 3 years later for $32 each. The annual return on investment is ________________________.
19. Payments of $25K per year are made over 4 years to pay off an $85K loan. The interest rate i is closest to
6% < i < 8% b) > 8% c) 4% < i < 6% d) < 4%
20. The sum 0f $2500 is deposited each quarter to a fund paying 2% per quarter. The number of payments required to amass $22K is at least
6 b) 7 c) 8 d) 9 e) 10
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