Question

Answer the following questions about interest rates and present values:
(a) Which interest rate (nominal or real) affects investment? Which affects money demand?
How do changes in the relevant interest rate affect these variables?
(b) A restaurant is considering remodeling. It estimates the remodel will cost $6,000 and
as a result revenues will rise by $3,000 the first year, $2,500 the second year, $1,500
the third year and have no effect in subsequent years. If the interest rate is 5%, should
the restaurant remodel? Support your answer.
(c) Suppose a household has a fixed rate mortgage. If the household pays $z each year,
starting this year, for the next 30 years, what is the present value of the mortgage
payments? Write your answer as a geometric series first (with 30 terms) and then
reduce it to a single term.

Answer 1

(a) A real interest rate takes inflation into account whereas a nominal interest rate does not take inflation into account.

Real interest rate = Nominal interest rate - Inflation

Inflation reduces the purchasing power of the consumer.Thus, we can say that it is the real interest rate that affects investment because nominal interest rate cannot tell the actual investment returns.

The demand for money is affected by nominal interest rates.

There is an indirect relation between interest rates and investment. If interest rates are high, people will borrow less and hence investment will decrease. Similarly if interest rates are low, people will borrow more which will increase the investment.

Money demand and interest rates also vary inversely.When money demand increases,interest rates fall down and when money demand decreases, interest rates rise.

(b) Interest rate = 5%

Remodeling cost =$6000

Interest for 3 years = (5% of $6000) * 3 = 300*3 = $900

Total cost = $6000+$900 = $6900

Total increase in revenue in 3 years = $3000+$2500+$1500 =$7000

As we can conclude that there are approximately no returns after the remodeling, so the restaurant should not be remodeled as per the profits are concerned.

(c) Let the fixed interest rate be 'i'

The household pays $z each year

Time period=30 years

Formula for calculating present value; PV=FV(1+i)^-n

Here,PV=Present value, FV=future value, i=interest rate, n= no of years.