Question

Debra plans to invest $2,250 for 10 years. She can invest in a savings account that pays 4% simple intrest or a savings account that pays 4% intrest compounded annually. How much more money will she have at the end of 10 years if she chooses the account with compound interest?

Answer 1

`\$180.55`

Explanation:

step 1

Simple interest

we know that

The simple interest formula is equal to

`A=P(1+rt)`

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

`t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04`

substitute in the formula above

`A=2,250(1+0.04*10)`

`A=2,250(1.4)`

`A=\$3,150`

step 2

Interest compounded annually

we know that

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

`t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04\\n=1`

substitute in the formula above

`A=2,250(1+(0.04)/(1))^(1*10)`

`A=2,250(1.04)^(10)`

`A=\$3,330.55`

step 3

Find the differences between the two final amounts

`A=\$3,330.55-\$3,150=\$180.55`