Question

1. You are expecting to receive the following payments: $2,000 in year 4, $8,000 in year 8. What is the present value of the two payments today, if the interest rate is 5%?

2. Assume you wish to accumulate $100,000 in year 8. You plan to deposit $20,000 today in a bank that guarantees an interest rate of 12%. What additional amount will you have to put in year 5 to achieve this target?

3. You deposited $3,000 in a bank ten years ago. The balance on your account is currently showing $7,102.09. What interest rate did the bank pay on your deposit?

4. You deposit $5,000 in bank today . What is the future value of the sum in year 10 if the interest rate is 6% in years 1-5 and 8% in years 6-10?

Answer 1

1)

$            7,060.12

Working:

Year

Cash flows

Discount factor

Present Value

a

b

c=1.05^-a

b*c

4

$                  2,000

0.823

$ 1,645.40

8

$                  8,000

0.677

$ 5,414.71

Total Present value

$ 7,060.12

2)

$          35,931.19

Working:

a.

Future Value of $ 20,000 in 8 years

=

20000*(1+0.12)^8

=

$ 49,519.26

b.

Balance required in year 8

=

$       1,00,000

-

$ 49,519.26

=

$ 50,480.74

c.

Now, amount to be deposited in year 5 will ne such so that that amount become in year 8 equivalent to

$ 50,480.74

d.

Amount to be deposited

=

$ 50,480.74

x (1.12^-3)

=

$ 35,931.19

(Since amount to be deposited is in year 5, it has 3 years of investment life)

3)

9%

Working:

FV

=

PV *(1+i)^n

Where,

$            7,102.09

=

3000*(1+i)^10

FV

$       7,102.09

2.3674

=

(1+i)^10

PV

$             3,000

2.3674^(1/10)

=

(1+i)

i

?

1.090

=

(1+i)

n

10

i

=

0.09

or , Interest rate is 9%

4)

$            9,831.46

Working:

Future Value

=

(5000*(1+0.06)^5)*((1+0.08)^5)

=

$       9,831.46