Question

the amount of $1,500 is invested at 7.5% for 4 years. compute the ending balance if the bank calculate simple interest. compute the ending balance if the bank calculate interest compounded annually. which is better investment simple interest or compound interest? how much more is earned?

Answer 1

Part 1

Simple interest

we know that

The simple interest formula is equal to

`A=P\mleft(1+rt\mright)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

P=$1,500

r=7.5%=0.075

t=4 years

substitute in the formula

`\begin{gathered} A=1,500(1+0.075\cdot4) \\ A=\$1,950 \end{gathered}`

Part 2

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$1,500

r=7.5%=0.075

t=4 years

n=1

substitute

`\begin{gathered} A=1,500(1+(0.075)/(1))^((1\cdot4)) \\ A=\$2,003.20 \end{gathered}`

therefore

A better investment is a compound interest

Find out the difference

2,003.20-1,950=$53,20

so

Is earned $53,20 more