Question

Problem 5 [Following questions are independent of each other]
a) If the inflation is 8% per year and the market interest rate paid by the bank is 12% per year, how much would be your real earning rate if you invest money into the bank?














b) Suppose that you rented your business property to receive the rent annually. At the end of each year you will receive 60,000 TL then-current money for 5 years. If the annual inflation rate is 5.77% and the real interest rate is 4%, determine the present worth of this income.















c) Suppose market interest rate is 12% and inflation rate is 4%. How much money should you invest now so that you have enough accumulated amount of money after 5 years to buy a car that is costing 100,000 TL today?

Answer 1

(a) Real Interest rate:
= (1 + Nominal Interest Rate) / (1 + Inflation Rate) - 1
= (1 + 0.12) / (1 + 0.08) - 1
= 1.12 / 1.08 - 1
=0.03703 ~ 3.70%
Thus, real earning rate is 3.70%

b) Computation of Present Worth (PW) at the nominal interest rate is as under:
60000 TL in real terms is received at the end of each year for 5 years.

Nominal interest rate = (1 + Inflation Rate) * (1 + Real Rate) - 1
= (1 + 0.0577) * (1 + 0.04) - 1
= 1.0577 * 1.04 - 1
= 0.100 ~ 10%

Present worth = Future value of annuity of 60000 TL for 5 years at 10%
= 60000 / 0.1 * (1.1^5 - 1)
= 366306 TL.

c) Value of car after 5 years:
= 100000 * 1.04^5
= 121665.29 TL

Value of investment (A) after 5 years:
A * (1.12)^5
A * (1.12)^5 = 100000 * (1.04)^5
A = 69036.15 TL
Thus, the amount invested today must be equal to 69036.15 TL.