Question

In: Finance

Because of a job change, Ben Hardesty has just relocated to the southeastern United States. He...

  1. Because of a job change, Ben Hardesty has just relocated to the southeastern United States. He sold his furniture before he moved, so he's now shopping for new furnishings. At a local furniture store, he's found an assortment of couches, chairs, tables, and beds that he thinks would look great in his new two-bedroom apartment; the total cost for everything is $3,000. Because of moving costs, Ben is a bit short of cash right now, so he's decided to take out an installment loan for $3,000 to pay for the furniture. The furniture store offers to lend him the money for 36 months at an add-on interest rate of 7 percent. The credit union at Ben's firm also offers to lend him the money - they'll give him the loan at an interest rate of 11.5 percent simple, but only for a term of 24 months.
  1. Compute the monthly payments for the loan from the furniture store. Round the answer to the nearest cent.   (1)

  1. Compute the monthly payments for the loan from the credit union. Round the answer to the nearest cent.  (1)
  1. Determine the APR for the loan from the furniture store. Do not round intermediate calculations. Round the answer to 2 decimal places.   (1)

d. Determine the APR for the loan from the credit union. Do not round intermediate calculations. Round the answer to 2 decimal places. (1)

Solutions

Expert Solution

Given:

Loan amount = $ 3000

Furniture Store offer:

Interest rate = 7% (Add-on Interest)

Tenure = 36 months = 3 years

Credit union Offer:

Interest rate = 11.5% (Simpe Interest)

Tenure = 24 months = 2 years

Solution a:

The monthly payments for the loan from the furniture store include add-on interest. Add-on interest refers to the calculation method of determining the total interest to be paid on a loan. This interest is added to the Principal and the total amount is divided by tenure to determine the monthly payment.

Interest payment = Principal * Annual Interest Rate * Tenure

Interest = 3000 * 7% * (36/12) = 630

Monthly Payments = (Principal + Interest ) / 36

=(3000 + 630) / 36

=3630 / 36

= 100.833

Hence, The monthly payments for the loan from the furniture store is 100.833

Solution b:

Monthly payments for the loan from the credit union: Simple Interest

In this case, Interest is chanrged only on the outstanding principal payments and not the whole Principal amount throughout the tenure.

This can be calculated using the PMT formula in Excel.

PMT(rate,nper, pv)

where, rate is the Interest rate per period = 11.5% / 12

nper is the number of periods = 24

pv is the present value of the Loan = 3000

PMT(11.5%/12,24,-3000) = 140.52

The Monthly Payment = $ 140.52

Solution c:

APR can be calculated using RATE function in Excel.

RATE(nper, pmt, pv),

wehre nper is the number of periods,

pmt is the Monthly installment,

pv is the present value of the loan

APR (Furniture Store) :

RATE(36, 100.833, -3000) = 1.07%

APR = 1.07% * 12 = 12.83%

APR for the loan from the furniture store is 12.83%

Similarly for the Crdit Store:

APR = RATE(24,140.52,-3000) * 12 = 0.96% * 12 = 11.50%

APR for the loan from the credit union is 11.50%

jeff jeffy answered 1 year ago
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