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# Interest Rates, TVM

You are given the following information
k*= 1%
Inflation rate is expected to be 2.5% for the next two years, 3% per year for the following two years, and 3.5% per year thereafter.
5 year US government securities have an interest rate that is 0.2% higher than 4 year US government securities
The MRP on 5 year securities is 0.40%
What is the MRP on 4 year US government securities?
6) You have the following five investment opportunities expressed in nominal rates of interest per year. You will be investing \$10,000 today. Which opportunity will yield the largest amount five years from today? Show how you derive your answer.

A) 7.000000% compounded annually
B) 6.881609% compounded semiannually
C) 6.823410% compounded quarterly
D) 6.784974% compounded quarterly
E) 6.766492% compounded daily
7) Your aunt has generously offered to pay the college tution/ room and board for your kid sister who will be starting school today. She will send a check for your sister's freshman year costsdirectly to the school. For remaining years, your aunt will deposit money in a savings account today from which your sister can withdraw the required funds one year, two year and three years from today. The bank pays interest of 2.5% per year, compounded annually. The college's tution/ room and board is \$33,000 for the current year and is expected to increase by \$2000 each year for the forsseable future. How much money does your aunt have to deposit in the bank today? How much will be in the account after your sister makes the second withdrawal two years from today?
a) How much money does your aunt have to deposit in the bank today?
b) How much will be in the account after your sister makes the second withdrawal two years from today?

#### Solution Preview

5) You are given the following information
k*= 1%
Inflation rate is expected to be 2.5% for the next two years, 3% per year for the following two years, and 3.5% per year thereafter.
5 year US government securities have an interest rate that is 0.2% higher than 4 year US government securities
The MRP on 5 year securities is 0.40%
What is the MRP on 4 year US government securities?

Year Inflation:
1 2.50%
2 2.50%
3 3%
4 3%
5 3.50%

Average inflation for 4 years= 2.75% =(2.5%+2.5%+3%+3%)/4
Average inflation for 5 years= 2.90% =(2.5%+2.5%+3%+3%+3.5%)/5

The determinants of interest rates are:

k = k* + IP + DRP + LP + MRP
where
k = required return on a debt security
k* = real risk-free rate of interest

Government securities do not have DRP and LP

5 year government security
k = k* + IP + MRP
where
k = required return on a debt security
k* = real risk-free rate of interest = 1.00%
IP = inflation premium = 2.90%
MRP = maturity risk premium = 0.40%
Thus k= 4.30%

interest rate on 5 year security= 4.30%

Return on 4 year ...

#### Solution Summary

The following posting calculates maturity risk premium and solves time value of money (TVM) questions.

\$2.19