Question

please show all the steps.

2) This question deals with nominal and real interest rates before and after taxation. Assume the following: i. Investor # 1 livse in 1980 when nominal interest rates were 12.7% and the inflation rate wils 10.1%. She has $10,000 to invest and faces a marginal tax rate of 40% Investor # 2 lives in 2000 when nominal interest rates were 5.4% and the inflation rate was 2.7%. She has $10,000 to invest and faces a marginal tax rate of 40% a) Determine the pre-tax real rate of return for both investors after 1 year b) After 1 year what is the nominal rate of return for both investors after tax? The real rate of return after taxes? c) After 1 year who is better off? Why?

Answer 1

a)Assume,Pre tax real rate of return =R

(1+R)*(1+Inflation Rate)=1+Nominal Interest Rate

For Investor 1:

Inflation Rate =10.1%=0.101

Nominal interest rate =12.7%=0.127

(1+R)*1.101=1.127

1+R=1.127/1.101=1.023615

R=Real Rate of Return =0.023615=2.36%

For Investor 2:

Inflation Rate =2.7%=0.027

Nominal interest rate =5.4%=0.054

(1+R)*1.027=1.054

1+R=1.054/1.027=1.02629

R=Real Rate of Return =0.02629=2.63%

b) Nominal Rate of return after tax:

For Investor 1:Nominal After tax Return =Pretax return *(1-Tax Rate )=Pretax Return *(1-0.4)=12.7*(1-0.4)=7.62%

For Investor 2: Nominal After tax Return =Pretax return *(1-Tax Rate )=Pretax Return *(1-0.4)=5.4*(1-0.4)=3.24%

Real Rate of Return after tax :

For Investor 1: Real After tax Return =((1+0.0762)/(1+0.101))-1=-0.02252=-2.25% (Negative Return)

For Investor 2: Real After tax Return =((1+0.0324)/(1+027))-1=0.005258=0.53% (Positive return)

Percentage figures are rounded to two decimal places

c) After one year Investor 2 is better off . Because investor 2 receives a positive inflation adjusted return. Investor 1 gets negative real return, which means that he looses money in real terms