Question

Seth is to pay bob 400 in the 4th year and 600 in the 8th year for a loan of 400. What is the Rate of Return that bob is getting? Interest is compounded monthly.

Answer 1

Answer

In order to calculate rate of return(r) we have to calculate r such that Present Value of amount Bob received is equal to Current value of loan.

Current value of Loan = 400

Present Value of amount after n years is given by :

PV = A/(1 + r/12)¹²ⁿ

where PV = present value, n = time period, r = rate of return.

Hence,

Net Present Value(NPV) = 400/(1 + r/12)⁴⁸ + 600/(1 + r/12)⁹⁶

Thus NPV= Current value of loan

=> 400/(1 + r/12)⁴⁸ + 600/(1 + r/12)⁹⁶ = 400

=> 2/(1 + r/12)⁴⁸ + 3/(1 + r/12)⁹⁶ = 2

Let (1 + r/12)⁴⁸ = t

=> 2/t + 3/t² = 2

=> 2t + 3 = 2t²

=> 2t² - 2t - 3 = 0

Solving this we get :

t = 1.822

=> (1 + r/12)⁴⁸ = 1.822

=> r = 0.1509 = 15.09%(approx)

Hence, Rate of return = 15.09%