Answered: What will be the balance at the end of…

Economics Today and Tomorrow, Student Edition

1st Edition

ISBN:9780078747663

Author:McGraw-Hill

Publisher:McGraw-Hill

Chapter6: Saving And Investing

Section6.1: Why Save?

Problem 6R

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Question

What will be the balance at the end of 5 years for $30,500 now at 10% annual interest, if compound interest is :
a. weekly b. continuously

Expert Solution

Step 1

Future value is the value of current cashflow at future date compounded at specified rate.

formula:

$F U T U R E V A L U E = P R E S E N T V A L U E \times {(1 + \frac{r}{m})}^{m \times n}$

where,

r=rate of interest

m=frequency of compounding

n= number of years

Step 2

given,

present value =$30,500

r=10%

n=5 years

m =52 (weekly compounding)

substituting values in formula:

$\begin{array}{rcl} F U T U R E V A L U E & = & P R E S E N T V A L U E \times {(1 + \frac{r}{m})}^{m \times n} \\ = & $ 30, 500 \times {(1 + \frac{0.1}{52})}^{52 \times 5} \\ = & $ 30, 500 \times 1 . 001923^{260} \\ = & $ 30, 500 \times 1.65 \\ = & $ 50261.86 \end{array}$

answer: $50261.86

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