Advertisements
Advertisements
प्रश्न
The compound interest payable annually on a certain sum for 2 years is Rs 40.80 and the simple interest is Rs 40. Find the sum and the rate percent.
Advertisements
उत्तर
Let sum be Rs. P and r % be the rate of interest.
We have t = 2 years, C.I. = Rs.40.80 and S.I. = Rs.40
Since, Simple interest
= `("P" xx "r" xx "t")/(100)`
⇒ 40 = `("P" xx "r" xx 2)/(100)`
⇒ Pr = `(4000)/(2)`
= 2000
Now,
C.I. = A - P
= `"P"(1 + "r"/100)^"t" - "P"`
= `"P"[(1 + "r"/100)]^"t" - 1]`
⇒ 40.80 = `"P"[(1 + "r"/100)^2 - 1]`
⇒ 40.80 = `"P"(1 + "r"^2/10000 + (2"r")/100 - 1)`
⇒ 40.80 = `"P"("r"^2/10000 + (2"r")/100)`
⇒ 40.80 = `"Pr"("r"/10000 + (2)/100)`
⇒ 40.80 = `2000(("r" + 200)/10000)`
⇒ 40.80 = `("r" + 200)/(5)`
⇒ r = 40.80 x 5 - 200
= 204 - 200
= 4
Hence, r = 4%
Now, Pr = 2000
⇒ P = `(2000)/"r"`
= `(2000)/(4)`
= 500.
Thus, sum is Rs.500 and rate of interest is 4%.
APPEARS IN
संबंधित प्रश्न
Calculate the amount and compound interest on Rs 10800 for 3 years at `12 1/2` % per annum compounded annually.
In how much time would Rs 5000 amount to Rs 6655 at 10% per annum compound interest?
In what time will Rs 1000 amount to Rs 1331 at 10% per annum, compound interest?
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.
The present population of a town is 28000. If it increases at the rate of 5% per annum, what will be its population after 2 years?
Rs. 8,000 is lent out at 7% compound interest for 2 years. At the end of the first year Rs. 3,560 are returned. Calculate :
(i) the interest paid for the second year.
(ii) the total interest paid in two years.
(iii) the total amount of money paid in two years to clear the debt.
The cost of a machine depreciated by Rs. 4,000 during the first year and by Rs. 3,600 during the second year. Calculate :
- The rate of depreciation.
- The original cost of the machine.
- Its cost at the end of the third year.
A man borrows Rs.10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 20% of the amount for that year. How much money is left unpaid just after the second year ?
Rachna borrows Rs. 12,000 at 10 percent per annum interest compounded half-yearly. She repays Rs. 4,000 at the end of every six months. Calculate the third payment she has to make at end of 18 months in order to clear the entire loan.
Find the sum on which the difference between the simple interest and compound interest at the rate of 8% per annum compounded annually would be Rs. 64 in 2 years.
A sum of Rs. 13,500 is invested at 16% per annum compound interest for 5years. Calculate :
(i) the interest for the first year.
(ii) the amount at the end of first year.
(iii) the interest for the second year, correct to the nearest rupee.
Calculate the amount and the compound interest on Rs. 10,000 in 3 years at 8% per annum.
Calculate the compound interest on Rs. 5,000 in 2 years; if the rates of interest for successive years be 10% and 12% respectively.
Rekha borrowed Rs. 40,000 for 3 years at 10% per annum compound interest. Calculate the interest paid by her for the second year.
A man invests Rs. 9600 at 10% per annum compound interest for 3 years. Calculate :
(i) the interest for the first year.
(ii) the amount at the end of the first year.
(iii) the interest for the second year.
(iv) the interest for the third year. the interest for the first year.
Rohit borrowed ₹ 40,000 for 2 years at 10% per annum C.I. and Manish borrowed the same sum for the same time at 10.5% per annum simple interest. Which of these two gets less interest and by how much?
Mr. Sharma lends ₹24,000 at 13% p.a. simple interest and an equal sum at 12% p.a. compound interest. Find the total interest earned by Mr. Sharma in 2 years.
Find the amount and the compound interest payable annually on the following :
Rs.25000 for 1`(1)/(2)` years at 10% per annum.
A man borrows Rs 62500 at 8% p.a., simple interest for 2 years. He immediately lends the money out at CI at the same rate and for same time. What is his gain at the end of 2 years?
If the present population of a city is P and it increases at the rate of r% p.a, then the population n years ago would be `"P"(1 + "r"/100)^"n"`
The time taken for ₹ 1000 to become ₹ 1331 at 20% p.a, compounded annually is 3 years
Find the C.I. on ₹ 15000 for 3 years if the rates of interest are 15%, 20% and 25% for the I, II and III years respectively
The number of conversion periods in a year, if the interest on a principal is compounded every two months is ___________
The time taken for ₹ 4400 to become ₹ 4851 at 10%, compounded half yearly is _______
Suppose a certain sum doubles in 2 years at r % rate of simple interest per annum or at R% rate of interest per annum compounded annually. We have ______.
A sum is taken for two years at 16% p.a. If interest is compounded after every three months, the number of times for which interest is charged in 2 years is ______.
Compound interest is the interest calculated on the previous year’s amount.
