Unit 4

Mathematics of Finance

Q1) Sushmita invested 5000rs. At the rate of 8 per cent per annum then what will be the value of the amount she invested in 5 years.

A1)

Here P = 5000, i = 8/100 = 0.08, n = 5, now

Hence the required amount is - 7000

Q2) Find out the simple interest on 5600 rs. At 12 percent per annum from July 15 to September 26, 2020.

A2)

Here we calculate the time-

Total days from july 15 to sept 26 = 73 days or 73/365 = 1/5 years

And P = 5600, i = 12/100 = 0.12

Simple interest = P.i.n. = 5600

Hence the simple interest is – 134.40

Q3) Harpreet invests 1200rs. At 10 percent per annum for some time and it becomes 1560 then find the principal when that will become 2232 at 8 percent p.a. in the same time.

A3)

Here in first situation- P = 1200, A = 1560 and i = 0.10

So that, 

In second situation-

A = 2232, n = 3, i = 0.08

Q4) Aman invests 1000 rupees at 5 percent p.a for four years then find the compound interest on it.

A4)

Here P = 1000, i = 0.05 and n = 4

Then we know that-

On taking log, we get-

Compound interest will be-

Which is the required answer.

Q5) A sum of money invested at C.I. payable yearly amounts to 10, 816 rs. at the end of the second year and to 11,248.64 rs. at the end of the third year. Find the rate of interest and the sum.

A5)

Here A1 = 10,816, n = 2, and A2 = 11,248.64, n = 3

We know that

 A = P (1 + i)n we get,

10,816 = … (i)

11,248.64 =… (ii)

Here on dividing equation (2) by (1)-

We get-

And

Hence the rate is 4 percent.

Now from first equation-

10,816 =

Or

Now-

P = antilog 4.000 = 10,000

Therefore the require answer- 10,000

Q6) Ronak deposited Rs. 10,000 in a bank for 3 years. Bank gives two offers either 10 percent compounded quarterly or 8% compounded continuously, then which offer is preferable for Ronak?

A6)

Balance after three years under first offer-

Balance after 3 years under second offer-

So that we can conclude that the first offer is preferable for Ronak.

Q7) Sundar decides to deposit 20,000rs. at the end of each year in a bank which pays 10% p.a. compound interest.

If the installments are allowed to accumulate, what will be the total accumulation at the end of 9 years?

A7)

Suppose A rs. be the total accumulation at the end of 9 years. Then we get-

Here P = 20,000 rs., i = 10/100 = 0.1 and n = 9

Then

Hence the total required accumulation is 2,71,590 rs.

Q8) Rajeev purchased a flat valued at 3,00,000rs. He paid 2,00,000 rs. at the time of purchase and agreed to pay the balance with interest of 12% per annum compounded half yearly in 20 equal half yearly installments.

If the first installment is paid after six months from the date of purchase, find the amount of each installment.

[Given log 10.6 = 1.0253 and log 31.19 = 1.494]

A8)

Here 2,00,000 has been paid at the time of purchase when cost of the flat was 3,00,000, we have to

consider 20 equated half yearly annuity payment P when 12% is rate of annual interest compounded half

yearly for present value of 1,00,000rs.

So that-

Or

Then-

Hence the amount of each installment  = 8,718.40

Suppose,

Taking log-

Hence

X = 0.3119

Q9) Rohan invests Rs. 5,000 in a term deposit plan. The plan offers an interest rate of 6% p.a., compounded quarterly. How much interest will John earn after one year? Also, what is the effective rate of interest?

A9) Here we have-

P = 5000, i = 6% per annum or 0.06 p.a. or 0.015 per quarter

Compounding period = n = 4

Rohan earns Rs. 306.82 interest after a year

Now the effective rate of interest is-

Q10) What is the effective rate of interest on a CD that has a nominal rate of 9.5 percent with interest compounded monthly?

Sol.

Here we have,

i = 9.5% or 0.095

Now the effective rate of interest is-

Q11) Amitabh invested Rs. 100 in a scheme that pays out a nominal annual interest rate of 10% compounded on a quarterly basis. Find the Effective Annual Rate.

A11)

Here we have,

i = 10% or 0.1

Now the effective rate of interest is-