Question

13. Phoebe realizes that she has charged too much on her credit card and has racked up $7,000 in debt. If she can pay $200 each month and the card charges 17 percent APR (compounded monthly), how long will it take her to pay off the debt? A. 28.63 months B. 35.00 months C. 47.71 months D. 48.68 months 14. What is the interest rate ofa 4-year, annual $1,000 annuity with present value of $3,500? A. 3.85 percent B. 5.56 percent C. 8.84 percent D. 9.70 percent 15. You wish to buy a $15,000 car. The dealer offers you a 4-year loan with a 9 percent APR What are the monthly payments? A. $260.78 B. $312.50 C. $373.28 D. $3,820.56 16. You are planning to make monthly deposits of $330 into a retirement account that pays 8 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 25 years? 1. $313838 2. $289499 3. $24124 4. $285992 17. What is the EAR of 14.9 percent compounded continuously? 1. 15.59 percent 2. 15.62 percent 3. 15.69 percent 4. 15.84 percent 5. 16.07 percent 18. Phil purchased a car today at a price of $8,500. He paid $300 down in cash and financed the balance for 36 months at 5.75 percent, compounded monthly. What is the amount of each monthly loan payment? 1. $248.53 2. $270.23 3. $318.47 4. $305.37 5. $257.62

Answer 1

13. We can use the present value of annuity (PVA) formula here,

$PVA=A\left [ \frac{(1+i/a)^{na})-1}{i/a(1+i/a)^{na}} \right ]$

Here,

A = Monthly payment

i = rate of interest

a = number of payments in a year

n = number of years

na = total number of payments (which we have to find)

$7000=200\left [ \frac{(1+0.17/12)^{na})-1}{0.17/12(1+0.17/12)^{na}} \right ]$

When you solve the above you will get na = 48.68 months.

(note to student: I can solve the above here, but it will show rounding off errors which will lead to more confusions. You can replace (1+0.017/12)^na with "x" and solve)

14.

We can use the same formula here to find the answer:

$PVA=A\left [ \frac{(1+i)^n-1}{i(1+i)^n} \right ]$

$3500=1000\left [ \frac{(1+i)^4-1}{i(1+i)^4} \right ]$

3.52(1+i)(1 i-1

or 5.56%

15.

Same formula

$PVA=A\left [ \frac{(1+i/a)^{na})-1}{i/a(1+i/a)^{na}} \right ]$

$15000=A\left [ \frac{(1+0.09/12)^{4*12}}{0.09/12(1+0.09/12)^{4*12}} \right ]$

$15000=A\left [ \frac{(1.0075)^{48}}{0.0075(1.0075)^{48}} \right ]$

$A=373.28$

Therefore, the monthly payments will be $373.28

16.

We have to use the formula for Future Value of Annuity (FVA)

$FVA = A\left [ \frac{(1+i/a)^{na}-1}{i/a} \right ]$

$FVA = 330\left [ \frac{(1+0.08/12)^{25*12}-1}{0.08/12} \right ]$

$= 330\left ( 951.0264 \right )$

Therefore the answer is $313,838