2. (50 points) You borrow $20,000 from a financial institution at an APR (annual
ID: 2439115 • Letter: 2
Question
2. (50 points) You borrow $20,000 from a financial institution at an APR (annual percentage rate) of 10% with interest being compounded annually. Payment Plan I: Pay in 5 installments, once per year, beginning a year from the date of borrowing. Each year, pay the accumulated interest as well as one fifth of the principal. Payment Plan 2: Pay in 5 installments, once per year, beginning a year from the date of borrowing. Each year, pay one fifth of the principal and $2,000. No other interest is charged. If you can borrow and lend at 10% in the market, which plan would you prefer?Explanation / Answer
When the interest is compounded annually, the formula of the Amount (A) is:
A = P{1+ (r/n)}nt where r is the interest rate, n is the number of times interest is compounded per year and t is the time in years.
In this case, since interest is compounded annually, n=1, t = 5 years and r=10% or 0.1. It is given that the principal amount P =$20000.
Therefore total amount payable at the end of 5 years is:
A= 20000{1+ (0.1/)}5
Or A= 20000*1.6051
Or A= $32210.20
Therefore interest accumulated in 5 years = $32210.20 - $20000 = $12210.20
For each year, the interest accumulated is $12210.20/ 5 = $2442.04
One fifth of the principal amount = $20000/5 = $4000.
Therefore at the beginning of the year, in Plan I, the instalment paid is: $2442.04+$4000 = $6442.04
Alternatively, in Plan II, one fifth of the principal amount = $4000 remains the same. Instead of the interest of $2442.04, only $2000 is required to be paid. It has been said that no other interest has been charged. Therefore at the beginning of the year in Plan II, the instalment paid is: $4000+$2000 = $6000.
The amount payable under the second plan is less than the amount payable under the first plan as $6000<$6442.04
Therefore when the interest is 10% and the person is a borrower, then plan II is preferable. If the person is a lender then plan I is preferable as the sum of instalments paid under plan I is greater than that under plan II.
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