Expert: Pawan Musale - 1/31/2011

Question
Compund growth:

 Suppose that $2,500 is invested at 7% compound quaterly. How much money will be in the account in:

A) 3/4 year?
B) 15 years?

Answer
Hello Sam

This is example of compound interest.

Compound interest is calculated as:

I = P * (1 + (r/100n))^nt   ------------------- (1)

Note: Read ^ in the above equation as 'to the power of' or 'raise to'

where I = Compound interest
P = Principal amount
r = Annual interest rate in percentage
n = number of times the interest is compounded per year
t = Total time duration (in years)

Now let us solve your questions.

(A)
P = 2500
r = 7
n = 4 (Quarterly means 4 times in a year)
t = 3/4 (or 0.75)

Putting these values in equation (1) above we get,

I = 2500 * (1 + (7/400))^(4*3/4)
 = 2500 * (1 + (7/400))^3
 = 2500 * (1 + 0.0175)^3
 = 2500 * (1.0175)^3
 = 2500 * 1.053 (Upto 3 decimals)
 = 2632.5

Hence total in the account after 3/4 year will be $2632.5.
Note: Answer will vary slightly depending on decimals you take into consideration

(B)
P = 2500
r = 7
n = 4 (Quarterly means 4 times in a year)
t = 15

Putting these values in equation (1) above we get,

I = 2500 * (1 + (7/400))^(4*15)
 = 2500 * (1 + (7/400))^60
 = 2500 * (1 + 0.0175)^60
 = 2500 * (1.0175)^60
 = 2500 * 2.83 (Upto 2 decimals)
 = 7075

Hence total in the account after 15 years will be $7075.
Note: Answer will vary slightly depending on decimals you take into consideration.

I hope this is clear now.

Kindly let me know if you need additional information.

All the best :)

Regards,
Pawan