Question

Show your calculations and answer the following questions

1. An investment will pay you $120 in one year and $200 in two years. Calculate the present value of these cash flows if the interest rate is 4%.

2. Suppose you invest $1000 in an account paying 6% interest per year. What is the balance in the account after 3 years? Calculate how much of this balance corresponds to “interest on interest”

3. If Brandon receives 6 percent interest rate on his bank account and the inflation rate is 4 percent. Calculate the real interest rate will he earn.

Answer 1

1) Statement showing present value

Year	Cash flow	PVIF @ 4%	PV
	A	B	C = A x B
1	120	0.9615	115.38
2	200	0.9246	184.91
Present value	300.30

Thus Present value = $300.30

2) Here formula of Future value can be used

FV = PV(1+r)^n

r = rate of interest = 6%

n = no. of years = 3

PV = $1000

Thus FV = 1000(1+6%)^3

=1000(1+0.06)^3

=1000(1.06)^3

=1000(1.1910)

= 1191.02 $

Thus after 3 years account balance will be 1191.02$

Now to find balance corresponds to “interest on interest”, one need to understand following

In first year Interest = 1000 x 6% = 60 $ thus balance = 1000+60 = $1060

In second year balance will be 1060 + (1000 x 6%) + (60 x 6%)

= 1060 + 60 + 3.6

= 1123.3

and third year balance will be 1123.3 + (1000 x 6%) + (123.3 x 6%)

=1123.3 + 60 + 7.42

=1191.02

Thus we can see that 3.6$ and 7.42$ is interest on interest

Thus  balance corresponds to “interest on interest = 3.6+7.42 = 11.02$

3) Real rate of interest = (1+ nominal rate of interest)/(1+ inflation rate) - 1
=(1+6%)/(1+4%) - 1
= (1+0.06)/(1+0.04) - 1
= 1.06/1.04 - 1
= 1.019231 - 1
= 0.019231
= 1.9231 %