Jocelyn is considering taking out one of the two following loans. Loan H is a three-year loan with a principal of $5,650 and an interest rate of 12.24%, compounded monthly. Loan I is a four-year loan with a principal of $6,830 and an interest rate of 10.97%, compounded monthly. Which loan will have the smaller monthly payment, and how much smaller will it be? Round all dollar values to the nearest cent.

The loan I have the smaller monthly which is $176.43 payment and loan I's monthly payment will be $11.88 smaller than Loan H's.

What is debt?

It is defined as the amount one party needs to pay to another party as the first party borrowed an amount which will credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.

We know the formula for the monthly payment:

[tex]\rm Monthly \ Payment \:=\:\dfrac{\left A\left(i\right)\left(1+i\right)^{n}\right}{\left(1+i\right)^{n}-1}[/tex]

For loan H:

Principal amount A = $5,650

Interest rate r = 12.24% = 0.1224

i = 0.1224/12 = 0.0102

Period = 3 years

n = 3×12 = 36

Compounded monthly.

After calculating:

Monthly payment for loan H= $188.31

For loan, I:

Principal amount A = $6830

Interest rate r = 10.97% = 0.1097

i = 0.1097/12 = 0.009141

Period = 4 years

n = 4×12 = 48

Compounded monthly.

After calculating:

Monthly payment for loan I = $176.43

Difference = $188.31—$176.43 = $11.88

Thus, the loan I have the smaller monthly which is $176.43 payment and loan I's monthly payment will be $11.88 smaller than Loan H's.

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