Question

A bank agrees to lend $10,000 now and $X 2 years from now in exchange for a single repayment of $75,000 at the end of 8 years. The bank charges interest at an annual effective rate of 4% for the first 3 years and at a force of interest ot - 1/ t + 1 for t2 3. Calculate X.

Answer 1

Let 'X' be the amount lend after 2 years

t = 3; so t+1 =4

So year is divided quarterly and interest is compounded quarterly after 3 years

(10000*(1.04)^3) + (X*1.04) + ((10000*(1.04)^3) + (X*1.04))*(1.01)^5^4) = 75000

11249+ 1.04X + (11249+ 1.04X)*1.2202 = 75000

13726+11249 +1.04X +1.2690X = 75000

2.309X = 50025

X = 21665

So the amount lend after 2 years is $21665.