Question

They decide to shop for furnishings for the new house. They choose items that amount to $3600.00. The store has 2 fixed installment loan options for purchasing: Option 1: 20% down payment and financing at 6% simple interest per year for 3 years. Option 2: no down payment and financing at 6.35% simple interest for 4 years. Answer each of the following questions separately, showing all your work to reach each answer.

A. Which option will result in smaller total finance charge? What will that total finance charge be?

B. Which option will result in the smaller monthly payment? What will that monthly payment be?

C. They decide to defer any purchases and invest a $3600 bonus that Maria will be getting from work in a savings account. The interest rate is 1.6% compounded every month. How much interest will they earn in 3 years?

D. They decide to defer any purchases and loan the $3600 bonus to a needy relative at 2.5% simple interest per year. How long will the term of the loan need to be if they want to earn $400 in interest (assuming the loan is not paid off early).

Answer 1

Amount = $ 3600

Option 01 :

20% Down Payment of Amount

Down Payment = 20% * Amount = 20% * 3600 = 720

Amount Borrowed = Amount - Down Payment = 3600 - 720 = 2880

Financing Charge = 6.00% Simple Interest Rate for 03 Years.

Financing Charge =  Amount Borrowed * Years * Interest Rate

= 2880 * 03 * 6% = 518.40

Monthly Payment = ( Borrowed Amount + Financing Charge) / Months = ( 2880 + 518.40) / ( 03*12)

= 3398.40 / 36 = 94.40

Option 02:

no down payment and financing at 6.35% simple interest for 4 years

Amount Borrowed = $ 3600

Financing Charge = Amount Borrowed * Years * Interest Rate

= 3600 * 04 * 6.35% = 914.40

Monthly Payment = ( Borrowed Amount + Financing Charge) / Months

= ( 3600+ 914.40) / ( 04*12) .

= 94.05

Ans A Option 01 will have Smaller Financing Charge. Total Finance Charge in Option 01: 518.40

Ans B Option 02  will result in a smaller monthly payment.  monthly payment in Option 02: 94.05

Amount Invested in Savings Amount A = 3600

Monthly Compounding Rate = 1.6%/12 = 0.016/12 = 0.00133

No of Months (n) = 3 YEARS * 12 = 36

Value after 03 Yeras F

F = 3600 * 1.04913 = 3776.893

Interest Earn = Future Value - Present value = F - A = 3776.893 - 3600 = 176.893

Ans C : They will earn interest of 176.893 (Ans)

Simple Interest Rate (r)  = 2.5% annual = 0.025

Interest (I)= 400

Principal = 3600

Time to earn 400 Interest = t

Interest = Principal * time * rate

400 = 3600 * t * 0.025

t = 400 / 90

t = 4.4444 Years

Ans D: The term of the loan should be 4.44 Years to earn $400 Interest.