Compact Disk Stereo

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1) Given A=P(1+I)^n

a) If P=$1200, I=.005, and n=30 Solve for A

$1,200(1.005)^30=1.1614 * 1,200=$1,393.68

b) If A=$5000, I=.0075, n=60 Solve for P

$5,000=P(1.0075)^60= 1.565681P=5,000

$3,193.50=P

2) Given 2500=1000(1.06)^n Solve for n

2.5=1.06^n Check: 2,500=1,000(1.06)^15.71

In 2.5 = (n) In 1.06 2,500=1,000(2.49785518249)

.916=.0583n

15.71=n

3) If you borrow $3000 at 14% simple interest for 10 months

A = P(1+rt)

a) How much will you owe in 10 months?

$3,000(1.14)(5/6))

$3,000(1.117)

$3,351

b) How much interest will you pay?

$3,351-$3,000=$351

4) A credit card company charges 22% annual rate for overdue accounts. How much interest will be owed on a $635 account one month overdue?

I = Prt

(635)(.22)(1/12)= 1/12=.083

$11.64

5) A loan of $2500 was repaid at the end of 10 months with a check for $2812.50. What annual rate of interest was charged?

A = P(1+rt) $2,812.50=$2,500(1+.83r)

$2,812.5=$2,500+$2,500(.83r)

$312.50=$2,500(.83r)

$312.50=$2,075r

.1506=r

15.06%

Compound Interest A = P(1+I)^n

6) Grandparents deposited $6000 into a grandchild’s account toward a college education. How much money will be in the account 17 years from now if the account earns 9% compounded monthly?

.09/12=.0075

17*12=

$6,000(1.0075)^204

$6,000(4.592)

=$27,552

7) What will an $8000 car cost 5 years from now if the inflation rate over that period averages 5% compounded annually?

8,000(1.05)^5

8,000(1.2763)=$10,210.40

8) How long will it take money to double if invested at 12% compounded monthly?

$2=$1(1 + .12)^n .12/12=.01

$2=1.01^n

In 2=(n) In 1.01

.6931=.00995n

n=69.66/12=5.8

9) ColorTime Rent To Own sells a compact disk stereo for $3000. You pay one third down and amortize the rest with equal payments over a 2 year period. If you are charged 1.5% interest per month on the unpaid balance

a) what is your monthly payment?

$3,000 (1.5) = 4,500 ==$126.96

1-(1 + .015)^-24 1-(1.015)^-24

b) How much interest will you pay over the 2 years?

$126.96 * 24 = $3,047.04

$3,047.04-$3,000

=$47.04

10) Two years ago you borrowed $10,000 at 12% interest compounded monthly, which was to be amortized over 5 years. Now you have acquired some additional funds and decide that you want to pay off this loan. What is the unpaid balance after making equal monthly payments for 2 years?

a) Find monthly payment

$10,000( .12) = 1,200 = $224.44

1-(1.01)^-2*12 1-(1.01)^-24

b) Find the present market value of $222.44 a month 5 year annuity

(3 years left)

222.44 1-(1 + .12)^-36 = 222.44 (1-(1.12)^-36) = $6,697.38

.12*3 36

11) Starting on his 21st birthday, and continuing on every birthday up to and including his 65th, Henry deposits $2000 a year into an IRA. How much will be in the account on his 65th birthday, if the account earns: (Hint: FV=)

a) 7% compounded annually...
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