# Time value of money

1. How long will it take double if invested at 12% compounded monthly?

2. Colortime Rent To Own sells a compact disk stereo for $3,000. 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?

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

3.Two years ago you borrow $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 the monthly payment

b) Find the present market value of $222.44 a month 5 year annuity (3 years left)

4.Starting on his 21st birthday, and continuing on every birthday up to and including his 65th, if the account earns:

a) 7% compounded annually

b) 11% compounded annually

5.A company established a sinking fund for plant retooling in 6 years at an estimated cost of $850,000.

a)How many should be invested semiannually into an account paying 8.76% compounded semiannually?

b)How much interest will you earn in the 6 years?

#### Solution Preview

1. How long will it take double if invested at 12% compounded monthly?

FV = PV(1 + i)n where FV is the future value

PV is the present value

i is the interest rate

n is the period

As this is the monthly payment, which divides the payment into 12 times per year, then, we need to divide the yearly interest by 12 and multiply the number of payment made by 12.

r = i/Periods per year

12%/12 = 0.01%

So, we will assume that the present value is 1 and the future value would be 2. Then, we will replace into the equation to find n.

2 = 1(1 + 0.01)n Solve for n

2 = (1 + 0.01)n

nLN(1.01) = LN(2)

n = LN(2)/LN(1.01)

= 0.6931/0.00995

= 69.65 months

or approximately 70 months.

You can use scientific calculator to find the log amount or use online calculator as follow.

http://www.math.com/students/calculators/source/scientific.htm

2. Colortime Rent To Own sells a compact disk stereo for $3,000. 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?

First, the amount to be amortized is only two third which is

$3,000 x 2/3 = $2,000

Then, we will use the annuity equation to find the monthly payment.

PVA = W x 1 - 1 where PVA is the present value

(1 + i)n W is the amount required monthly

i i is the interest rate

n is the period

As this is the monthly payment, which divides the payment into 12 times per year, then, we need to divide the yearly interest by 12 and multiply the number of payment made by 12.

Periods = Years x Periods per year

2 x 12 = 24

Then, ...

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