Accounting Problem

Question

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) 

Answer 1

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

 

Answer 2

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