Question

# Your friend wants to borrow money from you. He proposes to repay his debt in 5...

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).

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