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:

Option 1: 20% down payment and financing at 6% simple interest per year for 3 years.

This means that at the end of the 3 years you must pay an interest of $ 5,184.00 + $ 28,800.00 = $ 33,984.00 + $ 7,200.00 (initial 20%) In total they would pay $ 33,984.00 + $ 7,200.00 (initial 20%) = $ 41,184.00

 

Option 2: no initial payment and financing at 6.35% simple interest for 4 years.

This means that at the end of the 3 years you must pay an interest of $ 9,144.00 + $ 36,000.00 = $ 45,144.00

 

A. Which option will result in a lower total finance charge? What will be the total finance charge?

The lowest financial charge is offered by option 1 because even though the term for the total payment is only 3 years

B. Which option will result in a lower monthly payment? What will that monthly payment be?

The option that offers a lower monthly payment is option 1 for $ 144.00 monthly

C. They decide to defer any purchase and invest a $ 3,600 bond that Maria will receive from work in a savings account. The interest rate is 1.6% compounded each month. How much interest will they earn in 3 years?

Compound Interest = $ 6,374.94

D. They decide to defer any purchase and loan the $ 3,600 bond to a family member in need with a simple interest of 2.5% per year. How long will the loan term have to be if they want to earn $ 400 in interest (assuming the loan is not paid in advance)?

The time that must elapse is 4.44 years

Step-by-step explanation

Option 1: 20% down payment and financing at 6% simple interest per year for 3 years.

20%  $             7.200,00

80%  $          28.800,00

Note: The interest should be applied on 80% because 20% has already been paid

 

Simple Interest = Capital * Interest Rate * Time

Simple Interest = $ 28,800.00 * 6% * 3 years

Annual Simple Interest =  $             5.184,00

This means that at the end of the 3 years you must pay an interest of $ 5,184.00 + $ 28,800.00 = $ 33,984.00 + $ 7,200.00 (initial 20%) In total they would pay $ 33,984.00 + $ 7,200.00 (initial 20%) = $ 41,184.00

Option 2: no initial payment and financing at 6.35% simple interest for 4 years.

100%  $          36.000,00

Note: Interest should be applied on 100% because there is no initial payment

Simple Interest = Capital * Interest Rate * Time

Simple Interest = $ 36,000.00 * 6.35% * 4 years

Annual Simple Interest =  $  9.144,00

This means that at the end of the 3 years you must pay an interest of $ 9,144.00 + $ 36,000.00 = $ 45,144.00

A. Which option will result in a lower total finance charge? What will be the total finance charge?

The lowest financial charge is offered by option 1 because even though the term for the total payment is only 3 years, a smaller disbursement corresponding to $ 5,184.00 will be made at the end of 3 years, resulting in $ 1,728.00 for each year. The total payment to be made for the purchase will be $ 41,184.00

B. Which option will result in a lower monthly payment? What will that monthly payment be?

The option that offers a lower monthly payment is option 1 for $ 144.00 monthly

Monthly payment = $ 144.00 Annual Payment = $ 1,728.00

C. They decide to defer any purchase and invest a $ 3,600 bond that Maria will receive from work in a savings account. The interest rate is 1.6% compounded each month. How much interest will they earn in 3 years?

Capital  $             3.600,00

Interest rate 1.6%

Time in years 3 años

Time in months 36 meses

Important note: If the interest rate is expressed in months, the time must be expressed in the same way

Compound Interest = Principal * ((1+ (interest rate / 100)) ^ 36 months

Compound Interest = $ 3,600.00 * (1 + 0.016) ^ 36

Compound Interest = $ 3,600.00 * (1 + 0.016) ^ 36

Compound Interest = $ 3,600.00 * (1,016) ^ 36

Compound Interest = $ 3,600.00 * 1,770817

Compound Interest = $ 6,374.94

Note: To calculate the exponent in excel use the formula + Power (number; power)

D. They decide to defer any purchase and loan the $ 3,600 bond to a family member in need with a simple interest of 2.5% per year. How long will the loan term have to be if they want to earn $ 400 in interest (assuming the loan is not paid in advance)?

 

Capital = $ 3.600,00

Annual interest = 2,50%

Weather = ???

Expected interest = $ 400,00

Time = Expected interest / (Capital * Annual interest)

Time = $ 400 / ($ 3,600.00 * 2.50%)

Time = $ 400 / ($ 3,600.00 * 2.50%)

Time = $ 400 / $ 90

Time = 4.44 years

The time that must elapse is 4.44 years

PFA