Question

14. Suppose you deposit $200 into a bank for 1 year. At the time of your deposit, goods cost $2.50 apiece. A year later, you withdraw your deposit with interest, which totals $215. At that time, the price of goods has fallen to $2.40 apiece.a.What was the “real” value of your $200 at the time of your deposit?b.What nominal interest rate did your bank pay you for your deposit?c.What was the rate of inflation over the year that your money was sitting in the bank?d.What real interest ratedid you earn on your deposit?

Answer 1

a)

Real value of $200 at the time of deposit=Nominal value/Price level=200/2.50=80 units

b)

Future value of deposit=FV=$215

Present value of deposit=PV=$200

Number of periods=n=1 years

Nominal rate of interest paid by bank=(FV/PV)ⁿ-1=(215/200)¹-1=7.5%

c)

Rate of inflation=Change in price level/Initial price level=(2.40-2.50)/2.50=-4.0%

d)

Real value of $215 at the time of withdrawal=Nominal value/Price level=215/2.40=89.5833 units

Real interest rate realized=Change in real value/Initial Real value=(89.5833-80)/80=11.98%

We can also approximate real rate of interest realized as

Real interest rate=Nominal interest rate-inflation=7.5%+4%=11.5%