Question

After shopping for a car Amelia ended up borrowing $14300 from her grandparents at 7% per year compounded annually with repayment at the end of 5 years. Her Grandparents asked her to develop some alternative repayment options.

If Amelia's TVOM is 10%, what is the present worth for Amelia of each of the following 3 alternatives?

1) Interest only at the end of each year and principal at the end of the fifth year?

2) Equal annual payments?

3) Pay the principal and interest in one lump sum after 5 years?

If Amelia's TVOM is 4%, what is the present worth for Amelia of each of the following 3 alternatives?
1) Interest only at the end of each year and principal at the end of the fifth year?

2) Equal annual payments.

3) Pay the principal and interest in one lump sum after 5 years?

*This is being posted for the second time*

Answer 1

After shopping for a car Amelia ended up borrowing $14300 from her grandparents at 7% per year compounded annually with repayment at the end of 5 years. Her Grandparents asked her to develop some alternative repayment options.

If Amelia's TVOM is 10%, what is the present worth for Amelia of each of the following 3 alternatives?

Let the 10% is the rate of interest. (i = 10%)

P = 14300, i = 10%, n = 5 years

1) Interest only at the end of each year and principal at the end of the fifth year?

Interest will be 10% of 14300 = 1430 every year

PW = 1430 (P/A, 10%, 5) + 14300 (P/F, 10%, 5)

PW = 1430 (3.7908) + 14300 (0.6209) = 14300 (14299.7)

FV = 1430 (F/A, 10%, 5) + 14300

FV = 1430 (6.1051) + 14300 = 23030

2) Equal annual payments?

Annual payments (A) = 14300 (A/P, 10%, 5)

Annual payments (A) = 14300 (0.2638) = 3772

3) Pay the principal and interest in one lump sum after 5 years?

FV = 14300 (F/P, 10%, 5)

FV = 14300 (1.6105) = 23030

If Amelia's TVOM is 4%, what is the present worth for Amelia of each of the following 3 alternatives?

Let the 10% is the rate of interest. (i = 10%)

P = 14300, i = 10%, n = 5 years

Interest will be 4% of 14300 = 572 every year

PW = 572 (P/A, 4%, 5) + 14300 (P/F, 4%, 5)

PW = 572 (4.4518) + 14300 (0.8219) = 14300 (14299.6)

FV = 572 (F/A, 4%, 5) + 14300

FV = 572 (5.4163) + 14300 = 17398

2) Equal annual payments?

Annual payments (A) = 14300 (A/P, 4%, 5)

Annual payments (A) = 14300 (0.2246) = 3212

3) Pay the principal and interest in one lump sum after 5 years?

FV = 14300 (F/P, 4%, 5)

FV = 14300 (1.2167) = 17398