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QUESTION: 1

The compound interest on a certain sum for 2 years is Rs. 786 and S.I. is Rs. 750. If the sum is invested such that the S.I. is Rs. 1296 and the number of years is equal to the rate per cent per annum, Find the rate of interest?

Solution:

CI for 2 years = Rs. 786

SI for 2 years = Rs. 750

36/360 * 100 = 10%

P for first year = 3600

P*x*x/100 = 1296

x = 6%

QUESTION: 2

Hari took an educational loan from a nationalized bank for his 2 years course of MBA. He took the loan of Rs.5 lakh such that he would be charged at 7% p.a. at CI during his course and at 9% CI after the completion of the course. He returned half of the amount which he had to be paid on the completion of his studies and remaining after 2 years. What is the total amount returned by Hari?

Solution:

5,00,000 * (1.07)² = 572450

Returned amount = 286225

After two years = 286225 * (1.09)² = 340063

Total amount = 286225 + 340063 = 626288

QUESTION: 3

Rs.20,000 was invested by Mahesh in a FD @ 10% pa at CI. However every year he has to pay 20% tax on the CI. How much money does Mahesh have after 3 years?

Solution:

(20000*(1.08)³)=25194

QUESTION: 4

Leela takes a loan of Rs. 8400 at 10% p.a. compounded annually which is to be repaid in two equal annual installments. One at the end of one year and the other at the end of the second year. The value of each installment is?

Solution:

8400 = x*(210/121) ⇒ 4840

QUESTION: 5

A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs.723 more, if the interest was payable half yearly than if it was payable annually. The sum is ____

Solution:

sum – Rs.x

C.I. compounded half yearly = (4641/10000)x

C.I. compounded annually = (11/25)x

(4641/10000)x – (11/25)x = 723

x = 30000

QUESTION: 6

A sum of Rs.7140 is to be divided between Anita and Bala who are respectively 18 and 19 yr old, in such a way that if their shares will be invested at 4% per annum at compound interest, they will receive equal amounts on attaining the age of 21 year. The present share of Anita is

Solution:

Amount got by Anita after 3 yr = Amount got by Bala after 2 yr

x*(26/25)³ = (7140 – x)*(26/25)

26/25 = 7140 – x / x

x = 3500

QUESTION: 7

Suresh borrows Rs.6375 to be paid back with compound interest at the rate of 4 % pa by the end of 2 year in two equal yearly installments. How much will each installment will be?

Solution:

25x/26 + 625/676x = 6375

x = (6375 * 676)/1275 = 3380

QUESTION: 8

A sum of Rs. 8400 was taken as loan. This is to be paid in two equal annual installments. If the rate of interest be 20% compounded annually, then the value of each installment is

Solution:

Let value of each installment be X.

X/(1 + 20/100) + X/(1 + 20/100)² = 8400

⇒ X(5/6 + 25/36) = 8400

⇒ X(56/36) = 8400

X = 5400

QUESTION: 9

During the first year the population of a village is increased by 5% and the second year it is diminished by 5%. At the end of the second year its population was 31500. What was the population at the beginning of the first year?

Solution:

x * 105/100 * 95/100 = 31500

x = 31500 * 100/105 * 100/95

D = 31578

QUESTION: 10

If Rs. 7200 amounts to Rs.10368 at compound interest in a certain time , then Rs. 7200 amounts to what in half of the time?

Solution:

Let rate = R% and time = n year

Then, 10368 =7200(1+R/100)n

⇒ (1+R/100)n = 10368/7200 = 1.44

∴ (1 + R/100)n/2 = √1.44 = 1.2

∴ Required amount for n/2 yr

= 7200(1+ R/100)n/2

= 7200 x 1.2 = Rs. 8640

QUESTION: 11

A part of 70000 is lent out at 10% annum. The rest of the amount is lent out at 5% per annum after one year. The ratio of interest after 3 years from the time when first amount was lent out is 1:2. Find the second part that was lent out at 5%.

Solution:

10*3*x/5*2*y = 1/2

x/y = 1/6

6/7*70000 = 60000

QUESTION: 12

There is 50% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?

Solution:

In S.I,

Let P=100, I=50, T=5 yrs

R = 50*100/100*5 = 10%

In C.I, P = 12000, T=3 yrs, R= 10%

C.I = [12000*(1 + 10/100)^3 – 1 ] C.I = 3972.

QUESTION: 13

Karthik lends a certain amount to Vignesh on simple interest for two years at 20%. Vignesh gives this entire amount to Kamal on compound interest for two years at the same rate annually. Find the percentage earning of Vignesh at the end of two years on the entire amount.

Solution:

SI=20*2=40%

CI=20+20+(400/100)=44%

Diff = 44-40=4%

QUESTION: 14

A man borrows 3000 rupees at 10% compound interest. At the end every year he pays rupees 1000 back. How much amount should he pay at the end of the fourth Year to clear all his debt?

Solution:

After one year amount = 3000 *110/100 = 3300

He pays 1000 back, so remaining = 3300-1000 = 2300

After two year amount = 2300 *110/100 = 2530

He pays 1000 back, so remaining = 2530-1000 = 1530

After three year amount = 1530*110/100 = 1683

He pays 1000 back, so remaining = 1683-1000= 683

After fouth year = 683 * 110/100 = 751.3

QUESTION: 15

Rahul saves an amount of 800 every year and then lent that amount at an interest of 10 percent compounded annually. Find the amount after 3 years.

Solution:

800*(11/10)³=1064.8

800*(11/10)²=968

800*(11/10)=880

Total amount =2912.8

QUESTION: 16

Find the compound interest at the rate of 8% for 3 years on that principal which in 3 years at therate of 10% per annum gives 300 as simple interest.

Solution:

SI =300

Per yr = 100

Rate = 10%

C.I = 1000*(108/100)³ -1000

C.I = 259.712

QUESTION: 17

The difference between the total simple interest and the total compound interest compounded annually at the same rate of interest on a sum of money at the end of two years is Rs. 450. What is definitely the rate of interest per cent per annum?

Solution:

Difference = Pr /(100)^{2}

= (450×100×100)/(P×r^{2})

P is not given

QUESTION: 18

The CI on Rs.6000 for 3 years at 8% for first year, 7% for second year, 6% for the third year will be

Solution:

A = 6000*108/100*107/100*106/100

= 6000*1.08*1.07*1.06

= 7349.616 = 7350

CI = 7350-6000 = 1350

QUESTION: 19

Venkat and Vidhya have to clear their respective loans by paying 2 equal annual instalments of Rs.30000 each. Venkat pays at 10% pa of SI and Vidhyapays at 10% CI pa. What is the difference in their payments ?

Solution:

D =[(30,000 *110/100*110/100) – 30,000] – 30,000 *10*2/100

=[36300-30000]- 6000

=6300 – 6000

D = 300

QUESTION: 20

The difference between interest received by Vivek and Vimal is Rs.405 on Rs.4500 for 3 years. What is the difference in rate of interest ?

Solution:

4500*3/100(R1-R2) = 405

R1-R2 = 405*100/13500 = 3%

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