Question

You loan 3 people money, each agrees to pay you back at different times as follows,
the remaining time until 10 years you take the total (principal and interest) and you put it into a
safe savings plan with 2% interest compounded annually. How much interest do you get
combined with the three loans at the end of the 10 years?
a. Person A gets a $10,000 loan at 5% annually and will pay you back with interest in 3
years.
b. Person B gets a $5,000 loan at 4% annually and will pay you back with interest in 2
years.
c. Person C gets a $20,000 loan at 6% annually and will pay you back with interest in 6
years.

Answer 1

Answer
we need to calculate the all amounts after 10 years with two interest rates where interest changes in between and sum them all and then deduct the sum of all the initial amounts

interest amount =sum of future values with interest change - initial principal sum
sum of future values=sum of (PVi *(1+ri)^ni *(1+ji)^(p-n))

PVi=i th investment present value

ri=i th investment interest rate

ni=i th investment year
j is the second interest rate and the p-n where p=10 and n= initial lending term

interest amount =10000*(1.05^3)*(1.02^(10-3))+5000*(1.04^2)*(1.02^(10-2))+20000*(1.06^6)*(1.02^(10-6))-(10000+5000+20000)
=15342.8205262

the interest amount is $15342.82