**Exercise 14.3**

**1. On what sum will the compound interest at 5% per annum for 2 years compounded annually be Rs 164?**

**Solution:**

Let the sum be Rs x.

We know that:

Thus, the required sum is Rs 1600.

**2. Find the principal if the interest compounded annually at the rate of 10% for two years is Rs 210.**

**Solution:**

Let the sum be x.

We know that:

Thus, the required sum is Rs 1000

**3. A sum amounts to Rs. 756.25 at 10% per annum in 2 years, compounded annually. Find the sum.**

**Solution:**

Given,

Amount = Rs.756.25

Rate= 1=0% p.s

Time – 2 year

Let principal = P

So,

Hence,

Principal

Rs 625

**4. What sum will amount to Rs 4913 in 18 months, if the rate of interest is 12(1/2)% per annum, compounded half-yearly?**

**Solution:**

Let the sum be Rs x.

A = Rs 4913

R = 12.5%

N = 18 months = 1.5 years

We know that:

Thus, the required sum is Rs 4096.

**5. The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years is Rs 283.50. Find the sum.**

**Solution:**

It is given that

C.I – S.I = Rs 283.50

Rate of Interest = 15 %

n = 3 years(time)

suppose the sum is Rs y.

now we know that:

= 4000

Therefore, the sum is Rs 4000.

**6. Rachana borrowed a certain sum at the rate of 15% per annum. If she paid at the end of two years Rs 1290 as interest compounded annually, find the sum she borrowed.**

**Solution:**

Let the money borrowed by Rachana be x.

Then, we have:

Thus, Rachana borrowed Rs 4000.

**7. The interest on a sum of Rs. 2000 is being compounded annually at the rate of 4% per annum. Find the period for which the compound interest is Rs. 163.20.**

**Solution:**

Given,

Principal = Rs. 2000

Rate = 4% p.a

C.I= Rs. 163.20

Let time = t years

So,

= T = 2 years

Hence,

Time = 2years

**8. In how much time would Rs 5000 amount to Rs 6655 at 10% per annum compound interest?**

**Solution:**

Let the time period be n years.

Then, we have:

On comparing both the sides, we get:

n = 3

Thus, the required time three years.

**9. In what time will Rs 4400 become Rs 4576 at 8% per annum interest compounded half-yearly?**

**Solution:**

Let the time period be n years.

R = 8% = 4% (Half years)

Thus, we have:

On comparing both the sides, we get:

n = 1

Thus, the required time is half year.

**10. The difference between the S.I. and C.I. on a certain sum of money for 2 years at 4% per annum is Rs 20. Find the sum.**

**Solution:**

C.I – S.I = Rs 20

Principal = Rs 12500

Therefore, the required sum is Rs 12500

**11. In what time will Rs 1000 amount to Rs 1331 at 10% per annum, compound interest?**

**Solution:**

Let us assume the time to be t years.

So then,

Let us compare both the sides, we get:

n = 3 years

Therefore, the required time is three years.

**12. At what rate percent compound interest per annum will Rs. 640 amount to Rs. 774.40 in 2 years?**

**Solution:**

Given,

Principal = Rs 640

Amount = Rs 774.40

Time = 2 Year

Let rate = R%

So,

Hence,

Rate = 10% per annum

**13. Find the rate percent per annum if Rs 2000 amount to Rs 2662 in 1(1/2) years, interest being compounded half-yearly? **

**Solution:**

Let the rate of interest be R%

Then,

Because the interest rate is being compounded half-yearly, it is 20% per annum.

**14. Kamala borrowed from Ratan a certain sum at a certain rate for two years simple interest. She lent this sum at the same rate to Hari for two years compound interest. At the end of two years, she received Rs 210 as compound interest but paid Rs 200 only as simple interest. Find the sum and the rate of interest.**

**Solution:**

Let the sum be Rs P and the rate of interest be R%

We know that Kamal paid Rs 200 as simple interest.

200 =

Pr = 10000…(1)

Also, Kamla received Rs 210 as compound interest.

Putting the equation in (1), we get:

P = 1000

Thus, the required sum is Rs 1000 and the rate of interest is 10%

**15. Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in a year and a half, interest being compounded six monthly.**

**Solution:**

Given,

Principal = Rs.2000

Amount = Rs. 2315.25

= R = 10.25%

Hence,

Rate= 10.25%

**16. Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in a year and a half, interest being compounded six monthly.**

**Solution:**

Given,

Time = 3years

Let rate = R %

Let Principal = P

So, amount becomes = 2p

Rate = 25.99%

**17. Find the rate at which a sum of money will become four times the original amount in 2 years if the interest is compounded half-yearly.**

**Solution:**

Let the rate percent per annum be R.

So then,

Rate of Interest = 82.84

Therefore, the required rate is 82.84 %.

**18. A certain sum amounts to Rs 6832 in 2 years at 8% compounded interest. Find the sum.**

**Solution:**

Let the sum be P.

Thus, we have:

Thus, the required sum is Rs 5000.

**19. The difference between the compound interest and simple interest on a certain sum for 2 years at 7.5% per annum is Rs 360. Find the sum.**

**Solution:**

Let the sum be P.

Thus, we have

CI – SI = 360

P = 64000

Thus, the required sum is Rs 64000.

**20. The difference in simple interest and compound interest on a certain sum of money at 6% per annum for 3 years in Rs. 46. Determine the sum.**

**Solution:**

Given,

S.I – C.I = Rs. 46

Hence,

Principal = R. 3375

**21. Ishita invested a sum of Rs 12000 at 5% per annum compound interest. She received an amount of Rs 13230 after years. Find the value of n.**

**Solution:**

(1.05)^{n }=1.1025

(1.05)^{n }= (1.05)^{2}

On comparing both the sides, we get:

n = 2

Thus, the value of n is two years.

**22. At what rate percent per annum will a sum of Rs 4000 yield compound interest of Rs 410 in 2 years?**

**Solution:**

Let the rate percent be R.

We know that:

R = 5

Thus, the required rate percent is 5.

**23. A sum of money deposited at 2% per annum compounded annually becomes Rs 10404 at the end of 2 years. Find the sum deposited.**

**Solution:**

P = 10000

Thus, the required sum is Rs. 10000.

**24. In how much time will a sum of Rs 1600 amount to Rs 1852.20 at 5% per annum compound interest?**

**Solution:**

(1.05)^{n } = 1.157625

(1.05)^{n } = (1.05)^{3 }

If we compare both the sides, we get:

n = 3yrs

Therefore, the required time is 3 years.

**25. At what rate percent will a sum of Rs. 1000 amount to Rs. 1102.50 in 2 years at compound interest?**

**Solution:**

Given,

Principal = Rs. 1000

Amount = Rs. 1102.50

Time = 2 years

Let rate of interest = R% P per annum

So,

Hence,

Rate of interest = 5% per annum

**26. The compound interest on Rs 1800 at 10% per annum for a certain period of time is Rs 378. Find the time in years.**

**Solution:**

N = 2

Thus, the required both sides, we get:

n = 2

Thus, the required time is two years.

**27. What sum of money will amount to Rs 45582.25 at 6(3/4)% per annum in two years, interest being compounded annually?**

**Solution:**

Given,

Amount = Rs. 45582.25

Time = 2years

Let principal = Rs. P

So,

Hence,

Principal = Rs. 40000

**28. Sum of money amounts to. Rs 453690 in 2 years at 6.5% per annum compounded annually. Find the sum.**

**Solution:**

Thus, the required sum is Rs 400000.