Question

Mrs. Grey borrowed $5000 due in 18 months with interest at 6.50% compounded quarterly. The lender agrees to have her pay $1500 in four months, $1000 in one year and the balance in two years. If the money is worth 5.00% compounded monthly, calculate the payment two years from now that would liquidate Mrs. Greys debt.

Answer 1

Given that,

Mrs. Grey need to pay $5000 in 18 months.

interest rate r = 6.5% p.a. compounded quarterly

So, present value of this due = FV/(1+r/n)^(n*t) = 5000/(1+0.065/4)^(4*1.5) = $4539.07

The lender agrees to have her pay $1500 in four months, $1000 in one year and the balance in two years

new rate r = 5% p.a. compounded monthly

So, Present value of the new payments equals $4539.07

=> 4539.07 = 1500/(1+0.05/12)^4 + 1000/(1+0.05/12)^12 + X/(1+0.05/12)^24

=> 4539.07 = 1475.26 + 951.33 + 0.9050X

=> X = $2334.17

So payment 2 years from now is $2334.17