Question

Tyrone has $500 in his savings account. He wants to save more money. He is looking at two investment plans. Under plan A, he will increase his account balance by $100 a year. Under plan B, he will increase his account balance by 15% each year. How much more will he save with Plan B after 10 years?

Answer 1

`\$522.78`

Explanation:

Let

x ---> the number of years

y ---> the amount in the account balance

Plan A

we have a linear equation of the form

`y=mx+b`

where

The slope is equal to

`m=\$100\ per\ year`

The y-intercept or initial value is

`b=\$500`

substitute

`y=100x+500`

For x=10 years

substitute

`y=100(10)+500=\$1,500`

Plan B

we have a exponential growth function of the form

`y=a(1+r)^x`

where

`a=\$500\\r=15\%=15/100=0.15`

substitute

`y=500(1+0.15)^x`

`y=500(1.15)^x`

For x=10 years

substitute

`y=500(1.15)^(10)=\$2,022.78`

Find the difference of the two account balances after 10 years

`\$2,022.78-\$1,500=\$522.78`