A ten year loan of 10,000 at 8% annual effective can be repaid using any of the
ID: 2751472 • Letter: A
Question
A ten year loan of 10,000 at 8% annual effective can be repaid using any of the 4 following methods:
(I) Amortization method, with annual payments at the end of each year.
(II) Repay the principal at the end of ten years while paying the 8% annual effective interest on the loan at the end of each year. In addition, make equal annual deposits at the end of each year into a sinking fund earning 6% annual effective so that the sinking fund accumulates to 10,000 at the end of the 10th year.
(III) Same as (II), except the sinking fund earns 8% annual effective.
(IV) Same as (II), except the sinking fund earns 12% annual effective.
Rank the annual payment amounts of each method.
Explanation / Answer
(I) Amortization method, with annual payments at the end of each year.
Annual payments at the end of each year = Loan Amount/((1-(1+r)^-n)/r)
Annual payments at the end of each year = 10000/((1-(1+8%)^-10)/8%)
Annual payments at the end of each year = $ 1490.29
(II) Repay the principal at the end of ten years while paying the 8% annual effective interest on the loan at the end of each year. In addition, make equal annual deposits at the end of each year into a sinking fund earning 6% annual effective so that the sinking fund accumulates to 10,000 at the end of the 10th year.
Annual Interest Payment = Loan Amount*Interest Rate
Annual Interest Payment = 10000*8%
Annual Interest Payment = 800
Equal annual deposits at the end of each year into a sinking fund = Loan Amount/(((1+r)^n-1)/r)
Equal annual deposits at the end of each year into a sinking fund = 10000/(((1+6%)^10-1)/6%)
Equal annual deposits at the end of each year into a sinking fund = $ 758.68
Annual payments at the end of each year =Annual Interest Payment + Equal annual deposits at the end of each year into a sinking fund
Annual payments at the end of each year = 800 + 758.68
Annual payments at the end of each year = $ 1558.68
(III) Same as (II), except the sinking fund earns 8% annual effective.
Annual Interest Payment = Loan Amount*Interest Rate
Annual Interest Payment = 10000*8%
Annual Interest Payment = 800
Equal annual deposits at the end of each year into a sinking fund = Loan Amount/(((1+r)^n-1)/r)
Equal annual deposits at the end of each year into a sinking fund = 10000/(((1+8%)^10-1)/8%)
Equal annual deposits at the end of each year into a sinking fund = $ 690.29
Annual payments at the end of each year =Annual Interest Payment + Equal annual deposits at the end of each year into a sinking fund
Annual payments at the end of each year = 800 + 690.29
Annual payments at the end of each year = $ 1490.29
(IV) Same as (II), except the sinking fund earns 12% annual effective.
Annual Interest Payment = Loan Amount*Interest Rate
Annual Interest Payment = 10000*8%
Annual Interest Payment = 800
Equal annual deposits at the end of each year into a sinking fund = Loan Amount/(((1+r)^n-1)/r)
Equal annual deposits at the end of each year into a sinking fund = 10000/(((1+12%)^10-1)/12%)
Equal annual deposits at the end of each year into a sinking fund = $ 569.84
Annual payments at the end of each year =Annual Interest Payment + Equal annual deposits at the end of each year into a sinking fund
Annual payments at the end of each year = 800 + 569.84
Annual payments at the end of each year = $ 1369.84
Ranking:
IV ---------Rank 1
I and III-----------------Rank 2
II ----------------Rank 3
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