Question

1 point Carlos deposited $6,000 into an account that earned 3.75% simple interest for 6 years. How much more interest would the account have earned if it had earned compound interest instead of simple interest? Do not enter any spaces or commas. Round your answer to the nearest hundredths. mu $type your answer..

Answer 1

$133.07

Step-by-step explanation

Step 1

get the earned interest for 6 years

`I=\text{PRT}`

where I is the interest money created

P is the principal sarting amount of money

R is the rate per year(in decimal form)

T is the time,in years

then,let

P=$6000

R=3.75%=3.75/100=0.0375

time=t=6 years

now, replace.

`\begin{gathered} I=\text{PRT} \\ I=\text{\$}6000\cdot0.0375\cdot6\text{ } \\ I=1350 \end{gathered}`

It means Calos earned $1350 in the accoun with simple interest

Step 2

compound interest formula is given by

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

then, let

A= the amount after 6 years

P=6000

r=0.0375

t=6

replace,

`\begin{gathered} A=P(1+r)^t \\ A=6000(1+0.0375)^6 \\ A=7483.07 \end{gathered}`

to know, the money he earne do a subtraction

`\begin{gathered} I=7483.07-6000 \\ I=1483.07 \end{gathered}`

Step 3

finally, to know How much more interest would the account have earned if it had earned compound interest instead of simple interest do a subtraction

`\begin{gathered} \text{Answer}=1483.07-1350 \\ \text{Answer}=133.07 \end{gathered}`

so, the answer is $133.07

I hope this helps you