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

Answer:

$\ 522.78$

Step-by-step 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

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