Answer to Question #92251 in Financial Math for Nonzwakazi Makhonjwa

Question

R200000.he invested the full amount in a fixed deposit that pays interest at 7%p.a compounded monthly. The maturity date for his investment is 31December 2010.
The following annaul inflation rates have been predicted for the given calendar years
2008:8,3%
2009:8,5%
2010:8,7%
Without use of interest tables calculate the net present value for his investment.
Based on your npv calculations what is the implication of investing money when the nominal interest rate on fixed deposit is lower than the discount rate ?

Answer 1

For to have profit, the percentage benefits is more than percentage inflation rate. Any projects can be worthwhile or a worthy if NPV is positive

i)Suppose the person fixed deposited at first January of 2008. As bank offered interest rate of 7% annually compounded monthly, the total money get by the person at the end of 31 Dec., 2010 i.e. after 3 years or 36 months

$A=P(1+r/n)$^nt

A=200000(1+0.07/3)^12x3

A=R458,824.174

This the the NPV offered by bank after 3years

ii) Now as per average inflation rate which is calculated as (8.3+8.5+8.7)/3=8.5

Based on average inflation rate,

Total money to be after three years

$B=P(1+i)^t$

B=200000(1+0.085)³

B=R255,457.825

As A is greater than B after 3 years, there is the benefits get by person for fixed deposit.

It seem that normal interest rate offered by bank is less than inflation rate. But owing to provide the interest monthly and over it compounded monthly, NPV is positive. Means the project is worthy