Question

Calculate the present value of the compound interest loan. (Round your answers to the nearest cent.) $22,000 after 8 years at 3% if the interest is compounded in the following ways.

_________annually

__________quarterly

Find the effective rate of the compound interest rate or investment. (Round your answer to two decimal places.)

25% compounded monthly. [Note: This rate is a typical credit card interest rate, often stated as 2.1% per month.] ________%

Since 2007, a particular fund returned 13.9% compounded monthly. How much would a $4000 investment in this fund have been worth after 4 years? (Round your answer to the nearest cent.) ___________

In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the accumulated amount of the annuity. (Round your answer to the nearest cent.)

$2500 annually at 7% for 10 years. _____________

In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.)

$5500 yearly at 6% to accumulate $100,000. __________yr

Answer 1

1)

Annually:

Present value = Future value / ( 1 + r)ⁿ

Present value = 22,000 / ( 1 + 0.03)⁸

Present value = 22,000 / 1.26677

Present value = $17,367.0

Quarterly:

Rate = 3% / 4 = 0.75%

Number of periods = 8 * 4 = 32

Present value = 22,000 / ( 1 + 0.0075)³²

Present value = 22,000 / 1.270111

Present value = $17,321.3

2)

Effective annual rate = ( 1 + r/n)ⁿ - 1

Effective annual rate = ( 1 + 0.25/12)¹² - 1

Effective annual rate = 1.2807 - 1

Effective annual rate = 0.2807 or 28.07%

3)

Rate = 13.9% / 12 = 1.1583%

Number of periods = 4 * 12 = 48

Future value = Present value ( 1 + r)ⁿ

Future value = 4,000 ( 1 + 0.011583)⁴⁸

Future value = 4,000 * 1.738093

Future value = $6,952.4

4)

Future value = Annuity * [ ( 1 + r)ⁿ - 1] / r

Future value = 2,500 * [ ( 1 + 0.07)¹⁰ - 1] / 0.07

Future value = 2,500 * 13.816448

Future value = $34,541.1

5)

Time taken = 12.66 years

Keys to use in a financial calculator:

PMT -5500

FV 100000

I/Y 6

CPT N