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Accounting Problem

A principal of $6500 is invested in an account paying an annual rate of 7%.Find the amount in the account after 5 years if the account is compounded semiannuallly, quarterly and monthly. (show all work)
 
(A) The amount in the account after 5 years if the account is compounded semiannually. ( Round to the nearest cent)
 
(B) The amount in the account after 5 years if the account is compounded quarterly. (Round to the nearest cent)
 
(C) The amount in the account after 5 years if the account is compounded monthly. (Round to the nearest cent) 
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2 Answers

The formula is A=P(1+i/n)^(n*t) where A is the amount in the account, P in the initial principal, i is the nominal annual interest rate, n is the number of compounding periods per year, and t is the time in years.
 
A) A = 6500*(1+.07/2)^(10) = $9,168.89
B) A = 6500*(1+.07/4)^(20) = $9,196.06
C) A = 6500*(1+.07/12)^(60) = $9,214.56
This problem follows the investment equation: A = I(1+(r/n)^(nt) where
A = the amount after a certain time
I = the initial amount
r = the annual rate in decimal form
n = the number of times compounded per year
t = time in years
 
For each section of the problem, just plug the given numbers into the equation. 7% annual rate is 0.07 in decimal form. 
 
(A) A = 6500(1+(0.07/2))^(2*5)    [[Semiannually means it is compounded 2 times per year]]
A = 9,168.89 dollars
 
(B) A = 6500(1+(0.07/4))^(4*5)
A = 9,196.06 dollars
 
(C) A = 6500(1+(0.07/12))^(12*5)
A = 9,214.56 dollars
 

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