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Unit-3Interest and annuity 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 =

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) A man buys a machine for Rs.20,00. What its value be after 6 years, if it is assumed to depreciate at a fixed rate of 12% per annum.

A7)

Here we have P = 20,000, n = 6 and r = -0.12 (rate of interest is negative in depreciation)

Then,

So that the value of the machine in 6 years will be = 9288.08

Q8) A machine valued at 500,000 depreciates at 6% per annum then in how many year its value will reduce to 100,000?

A8) Here P = 500,000, r = 0.06, n = ? and the final value is = 100,000

We know that-

Taking log on both sides-

So that-

Therefore approximately it will take 26 years for the value decline to 100,000

Q9) Ayesha invests Rs. 3000 initially and then Rs. 1800 at the end of the first, second and third years and finally Rs. 600 at the end of 4th year.If the interest is paid annually at the rate of 6.5% then find the value of the investment at the end of 5th year.

A9)

Rs. 3000 is invested for 5 years and grows to-

The three sums of Rs. 1800 are invested for 4, 3 and 2 years and grow in total-

And Rs. 600 is invested for 1 year and grows to-

Then the total value at the end of 5 years will be 11,280.81

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