Question

Question No : 3

- If you deposit 10 $ in an account, that pays 5% interest, compounded annually, how much you will have at the end of 10 years? 50 years and 100 years
- How much will be in account at the end of 5 years the amount deposited today is 10,000 and interest is 8% per year, compounded semiannually?
- How much would I have to deposit in an account today that pays 12% interest, compounded quarterly, so that I have a balance of 20,000 in the account at the end of 10 years?
- Suppose you deposit 1,00,000 in an account today that pays 6% interest compounded annually. How long does it take before the balance in your account is 5,00,000?
- At what interest rate an investment of 12,000 be compounded annually to become 28,000 in 12 years?

Answer #1

a. | Deposit Amount= | 10 | ||

Interest Rate = | 5% | Annual Compounding | ||

Value of deposits at the end of - | ||||

10 Years
= |
10x(1+0.05)^10 = | 16.29 | ||

50 Years
= |
10x(1+0.05)^50 = | 114.67 | ||

100 Years
= |
10x(1+0.05)^100 = | 1,315.01 | ||

b. | Deposit Amount= | 10,000 | ||

Interest Rate = | 8% | Semi-Annual Compounding | ||

Value of deposits at the end of - | ||||

5 Years = |
10000 x (1+(0.08/2))^(5x2) = | |||

10000 x 1.04^10 | ||||

14802.44 | ||||

c. | Deposit Amount= | A | ||

Interest Rate = | 12% | Quarterly Compounding | ||

Value of deposits at the end of - | ||||

10 Years
= |
20000 | |||

20000= | A x (1+(0.12/4))^(10x4) = | |||

20000= | A x 1.03^40 = | |||

20000= | A x 3.2620 = | |||

A = | 20000/3.2620 | |||

A = | 6131.14 | |||

d. | Deposit Amount= | 1,00,000 | ||

Interest Rate = | 6% | Annual Compounding | ||

Value of deposits at the end of x years = 500000 | ||||

100000 x (1+0.06)^X = | 500000 | |||

1.06^x = | 500000/100000 = 5 | |||

At x = 27 | 4.82 | |||

At x = 28 | 5.11 | |||

Therefore it will take 28 years to reach 500000 | ||||

e. | Deposit = | 12000 | ||

Rate = | r | Annual Compounding | ||

Value at the end of 12 years = | 28000 | |||

12000 x (1+r)^12 = | 28000 | |||

(1+r)^12 = | 28000/12000 | |||

(1+r)^12 = | 2.33 | |||

Using Linear Interpolation - | ||||

7% | 2.25 | |||

r | 2.33 | |||

6% | 2.01 | |||

(r-6)/(7-6) = | (2.33-2.01)/(2.25-2.01) | |||

r-6 = | 0.33809748 | |||

r= | 6.34 | |||

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