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To pay for a home improvement project that totals $11,000, Genesis is choosing between taking out a simple interest bank loan at 6% for 3 years or paying with a credit card that compounds monthly at an annual rate of 16% for 6 years. Which plan would give Genesis the lowest monthly payment?

The monthly credit card payment would be $396.49, which is lower than the monthly payment on the bank loan.
The monthly payment on a bank loan would be $360.56, which is lower than the monthly credit card payment.
The monthly credit card payment would be $354.44, which is lower than the monthly payment on the bank loan.
The monthly payment on a bank loan would be $323.89, which is lower than the monthly credit card payment.



Answer :

The monthly payment on a bank loan would be $360.56, which is lower than the monthly credit card payment.

What is the monthly payment under simple interest?

The total interest on the simple interest basis can be determined as the cost of the home improvement multiplied by the annual simple interest rate and also multiplied by the number of years

I=PRT

I=interest for 3 years=unknown

P=principal=$11,000

R=simple interest rate=6%

T=number of years=3

I=$11000*6%*3

I=$1980

There are 12 months multiplied by 3 years

monthly payment=($11,000+$1,980)/(3*12)

monthly payment=$360.56

Monthly compounding option:

PV=PMT*(1-(1+r)^-N/r

PV=loan amount=$11,000

PMT=monthly payment=unknown

r=monthly interest rate=16%/12=0.0133333333333333

N=number of monthly payments in 6 years=12*6=72

$11,000=PMT*(1-(1+0.0133333333333333)^-72/0.0133333333333333

PMT=$238.61

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