Question

calculations and round the final answer to 2 decimal places. Total possible márkš tor se Adam borrowed S5000 today at 10% compounded semi-annually. He decided to repay S2000 in two years and 52500 in three years. How much will he still owe in five years

Answer 1

Here we have to calculate the present value of the payments and then compare it to borrowed amount.

Here interest rate = 10% /2 = 5% or 0.05
N will time period in semiannual payments = for $2000 = 2 years * 2 = 4 and for $2500 = 3 years * 2 = 6
Present value of payements= $2000 / ( 1 +0.05)^4 + $2500 / ( 1 +0.05)^6
= $2000 / 1.2155 + $2500 / 1.3401
= $1,645.41 + $1,865.53
= $3,510.94

Loan borrowed = $5000
Amount still owe = $5000 - $3,510.94 = $1,489.06
This amount still owe is in present value i.e. value on today which is to be paid in future along with interest.
Amount he still owe in 5 years = $1,489.06 * (1.05)^10
= $1,489.06 * 1.6289
= $2,425.53