Question

After shopping for a car Amelia ended up borrowing $13200 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 12%, 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?

Answer 1

Answer:.

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