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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...
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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