Question

Your friend wants to borrow money from you. He proposes to repay his debt in 5 monthly installments of $200, starting from month 4 (i.e., the first payment will occur at the end of month 4). If the monthly interest rate on your savings account is 1%, how much would you lend your friend at most? Round your result to the nearest cent, and do not use a $ sign (i.e., if the result is $1012.4671, enter it as 1012.47).

Answer 1

Amont lend to friend at most will be present value of repayment made by friend.

Amount repaid per month = 200

Repayment starts from end of month 4

Number of payments (n) =5

monthly interest rate (i)=1%

Present value of payment at month 3 = Annuity at end *(1-(1/(1+i)^n))/i

=200*(1-(1/(1+1%)^5))/1%

=$970.69

This is value at month 3 end (future value) = $970.69

month gap (n) =3

Present value of single future value today = future value/(1+i)^n

=970.69/(1+1%)^3

=$942.14

So we can land our friend at most $942.14