Question

The car you wish to purchase, costs $12000 today. A bank has a deposit account for the purchase of automobiles with an interest of 12% anually. It is expected that the cost of the car will increase at a rate of 3% anually.

a. Indicate the inflation rate

b. Indicate what is the market rate

c. Indicate what is the real interest rate

d. Determine the cost of the car in 5 years

e. Determine how much you will need to deposit in the account today in order to be able to purchase the car in 5 years.

Include steps please, thank you.

Answer 1

Hi,

I hope you are doing well!

Question:

Answer:

a).

Inflation rate= 3%

Inflation Rate- The inflation rate is the rate at which the general rise in the level of prices, goods and services in an economy. Here price of car will increase at the rate of 35 annually.

b).

Market rate= $12000

Market rate is the current value of goods or services.

c).

Real Intrest rate is 9%

Real interest rate is adjusts the observed market interest rate for the effects of inflation. It means real interest rate equal to nominal interest rate - inflation.

d).

In this question we have to calculate the future value of car ( value of car after the adjustment of inflation).

FV= PV (1 + r)^n

Where, PV = Present Value

t = discount rate( inflation rate)

t = time

FV = 12000( 1+3%)^5

= 12000(1.03)^5

FV = 12000(1.159) = $13911

So, the value of car will be $13911 after 5 years.

e).

In this question we have to calculate the the PV of car-

FV = 13911

discount rate = 12%

t = 5 years

PV = FV/(1+r)^n

= 13911/(1+12%)^5

= 13911/(1+12/100)^5

= 13911/(112/100)^5

= 13911/(1.12)^5

= 13911/1.762 = 7895

PV = $7895

So, have to invest $7895 at 12% interest rate for 5 years to buy that car.

Thank You