Question

Mahesh graduated from college six years ago with a finance undergraduate degree. Although he is
satisfied with his current job, his goal is to become a banker. He feels that MBA degree would allow
him to achieve this goal. After examining business schools, he has narrowed his choice to Kathmandu
University, school of management, one of the renowned University in Nepal. Although internships are
encouraged by the school, to get class credit for the internship, no salary can be paid. Other than
internship, neither school will allow its students to work while enrolled in its MBA program. Assume
it is now January 1, 2020 and he is planning to accumulate Rs 710,000 including college fees and other
stationery expenses for an MBA in January 2025. Today he is thinking for a deposit in a bank that pays
11 per cent nominal interest rate. The source of income that he received quarterly from his current job
is Rs 65,000. Out of his quarterly income he spends 65 per cent amount for his living. His mother has
also deposited Rs 200,000 in his account to facilitate his MBA degree. In order to attain his goal, you
are required to answer the following: [1+2+2+2+1+2=10]
a. How much must he deposit in lump sum on January 1, 2020 to accumulate a university fees along
with stationery expenses of Rs 710,000 on January 1, 2025?
b. If Mahesh wants to make equal installments on each January 1 from 2021 through 2025, how large
must each payment be?
c. If he wants to invest his quarterly salary net saving in the bank, the first payment being made at the
end of first quarter from now, how much he could accumulate in January 1, 2025? Assuming that
interest is compounded on quarterly basis.
d. What is the effective annual rate if interest is compounded monthly? Explain the difference
between annual percentage rate and effective annual rate.
e. If his bank balance of Rs 200,000 today pays 9 per cent annual interest compounded monthly, to
which value it will grow on January 1, 2025?
f. A dollar in hand today is worth more than a dollar to receive next year. Give your arguments.

Answer 1

ONLY FIRST 4 SUB PARTS ANSWERED:

Ans-(a)

Here it is assumed that 11% rate of interest will be given by the deposit and each year interest earnings shall be reinvested i.e annual compounding.

Basis the above the lump sum amount that Mahesh needs to deposit on 1st Jan2020 to have a corpus of 710000 on 1st Jan,2025 can be derived by using the following formula :

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

P - Lump sum to be deposited today

A - Target amount here 710000

r - rate of Interest

n - number of times interest applied in a period here 1 since annual

t - number of time periods elapsed here 5 years

Applying thev values in the above equation

P = 710000 / (1+11%)^5 = 421350

He needs to deposit an amount of Rs 421350 today

Ans-(b)

If equal annual payments to be made to achieve te target amount of 710000 the amount to be annualy deposited can be found out using te following formula

A = FV*r/[(1+r)^n-1]

A - Annual deposits

FV - Future value , here 710000

r - rate of Interest i.e. 11%

n - periods , here 5 years

Putting the values in te formula

A = 710000*11%/[(1+11%)^5-1] = 78100/0.685058 = 114005

This will give him a corpus of 710000 as on 1Jan2025 (including 1Jan2025 deposit)

Ans-(c )

Quarterly Savings of Mahesh = 65000*35% = 22750

If this amount is invested everu quarter then on on 1jan2025 he will have fund of Rs 595991.

This can be arrived at by the following formula application -

FV = PMT[(1+ i/m)^mY-1]/(i/m) = 22750[(1+11%/4)^20-1]/(11%/4) = 595991

where

FV - Future value i.e value on 1Jan2025

PMT - periodic payment , here it is 22750

i - Interest rate , 11%

m - compounding periiod i.e. every quarter 4

Ans-(d)

Effective rate of Interest for monthly compounding when stated rate is 11% would translate into 11.57% calculated as

EIR = (1+i/m)^m-1 = (1+11%/12)^12-1 = 11.57%

i - is the rate of interest , 11% here

m - number of compoundinigs in a year

The difference between Effective Interest rate and annual Interest rate is of the component of "Interest earned on Interest' during the period.In cas eof annual Interest Interest accrues at year end meaning the principal is constant till year end.When the compounding is say monthly ten at each month end te principal increases by te amount of te interest of the month and in subsequent month interest gets calulated on the amount and so on.Hnece there is extra interest earned during te period on te interest accrued from previous period.Hence effec tive rate of Interest is higher ten stated rate.