# Interest Problems

• May 28th 2008, 12:59 PM
VDestinV
Interest Problems
I need to use the formula

PV=A/(1+i)^n

where:
PV is the present value
A is the final amount
i is the interest per compounding periods
n is the number of compunding periods

Now the question is:

An investment grows from $600 to$1200 in 9 years. If the interest was compounded monthly, what was the annual rate?
• May 28th 2008, 01:46 PM
janvdl
Quote:

Originally Posted by VDestinV
I need to use the formula

PV=A/(1+i)^n

where:
PV is the present value
A is the final amount
i is the interest per compounding periods
n is the number of compunding periods

Now the question is:

An investment grows from $600 to$1200 in 9 years. If the interest was compounded monthly, what was the annual rate?

$A = P \left( 1 + \frac{i}{100} \right) ^{n}$

$1200 = 600 \left( 1 + \frac{i}{100} \right) ^{9 \times 12}$

$1200 = 600 \left( 1 + \frac{i}{100} \right) ^{108}$

$2 = \left( 1 + \frac{i}{100} \right) ^{108}$

$\sqrt[108]{2} = 1 + \frac{i}{100}$

$i = 100 \left( \sqrt[108]{2} - 1 \right)$

This gives you the monthly rate.

$12 \times i = 7.73$
That would be the annual rate.