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## Chris borrows 450 dollars from Gavin. Gavin lets Chris choose either a simple interest loan for 10 years with a 3.5% interest rate or loan c

Question

Chris borrows 450 dollars from Gavin. Gavin lets Chris choose either a simple interest loan for 10 years with a 3.5% interest rate or loan compound annually for 7 years with a 2% interest rate. Which should Chris choose if he wants the cheaper plan?

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Mathematics
3 years
2021-08-19T04:09:48+00:00
2021-08-19T04:09:48+00:00 1 Answers
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## Answers ( )

Answer:

Chris should go for the LOAN THAT IS COMPOUNDED ANNUALLY because the interest rate is lower compared to the simple interest

Step-by-step explanation:

Chris borrows 450 dollars from Gavin.

Step 1

We find Simple Interest

Gavin lets Chris choose either a simple interest loan for 10 years with a 3.5% interest rate

Formula = P × R × T

= 450 × 3.5% × 10

= $157.5

Step 2

We find compound interest

loan compound annually for 7 years with a 2% interest rate.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 rate per year,

Then solve the equation for A

Formula:

A = P(1 + r/n)^nt

A = 450.00(1 + 0.035/1)(1)(7)

A = 450.00(1 + 0.035)(7)

A = $572.53

Interest = A – P where

P (principal) = $450.00

I = $572.53 – $450.00

I (interest) = $122.53

Which should Chris choose if he wants the cheaper plan?

Comparing the calculations above, Chris should go for the Loan that is compounded annually because the interest rate is lower compared to the simple interest