Question

Megan has $15,000 to invest. She is considering two investment options. Option A pays 3.2% simple interest. Option B pays 4.1% interest compounded annually. What is the value of each investment option at 10 years?

Answer 1

wheee

Compute each option

option A: simple interest

simple interest is easy

A=I+P

A=Final amount

I=interest

P=principal (amount initially put in)

and I=PRT

P=principal

R=rate in decimal

T=time in years

so given

P=15000

R=3.2% or 0.032 in deecimal form

T=10

A=I+P

A=PRT+P

A=(15000)(0.032)(10)+15000

A=4800+15000

A=19800

Simple interst pays $19,800 in 10 years

Option B: compound interest

for interest compounded yearly, the formula is

`A=P(1+r)^t`

where A=final amount

P=principal

r=rate in decimal form

t=time in years

given

P=15000

r=4.1% or 0.041

t=10

`A=15000(1+0.041)^(10)`

`A=15000(1.041)^(10)`

use your calculator

A=22418.0872024

so after 10 years, she will have $22,418.09 in the compounded interest account

in 10 years, the investment in the simple interest account will be worth $19,800 and the investment in the compounded interest account will be worth$22,418.09