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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Ngọc Diệp 3 years 2021-08-19T04:09:48+00:00 1 Answers 100 views 0

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    2021-08-19T04:11:16+00:00

    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

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