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.
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 18000 for `2 1/2` years at 10% per annum compounded annually.
Calculate the amount and compound interest on Rs 62500 for `1 1/2` years at 8% per annum compounded half yearly.
Calculate the amount and compound interest on Rs 8000 for 1 year at 9% per annum compound half yearly. (You could use the year by year calculation using SI formula to verify)
Simple interest on a sum of money for 2 years at \[6\frac{1}{2} %\] per annum is Rs 5200. What will be the compound interest on the sum at the same rate for the same period?
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.
In what time will Rs 1000 amount to Rs 1331 at 10% per annum, compound interest?
At what rate percent per annum will a sum of Rs 4000 yield compound interest of Rs 410 in 2 years?
A certain sum amounts to Rs. 5,292 in two years and Rs. 5,556.60 in three years, interest being compounded annually. Find: the original sum.
The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1,089 and for the third year it is Rs. 1,197.90. Calculate the rate of interest and the sum of money.
Geeta borrowed Rs. 15,000 for 18 months at a certain rate of interest compounded semi-annually. If at the end of six months it amounted to Rs. 15,600; calculate :
(i) the rate of interest per annum.
(ii) the total amount of money that Geeta must pay at the end of 18 months in order to clear the account.
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.
Ashok borrowed Rs. 12,000 at some rate on compound interest. After a year, he paid back Rs.4,000. If the compound interest for the second year is Rs. 920, find:
- The rate of interest charged
- The amount of debt at the end of the second year
On a certain sum of money, lent out at C.I., interests for first, second and third years are Rs. 1,500; Rs. 1,725 and Rs. 2,070 respectively. Find the rate of interest for the (i) second year (ii) third year.
Calculate the amount and the compound interest on Rs. 10,000 in 3 years at 8% per annum.
A certain sum of money invested for 5 years at 8% p.a. simple interest earns an interest of ₹ 12,000. Find:
(i) the sum of money.
(ii) the compound interest earned by this money in two years and at 10% p.a. compound interest.
Find the difference between simple and compound interest on Rs 5000 invested for 3 years at 6% p.a., interest payable yearly.
The compound interest on ₹ 8000 at 10% p.a for 1 year, compounded half yearly is ____________
The annual rate of growth in population of a town is 10%. If its present population is 26620, then the population 3 years ago was _________
If the compound interest is calculated quarterly, the amount is found using the formula __________
The difference between the C.I and S.I for 2 years for a principal of ₹ 5000 at the rate of interest 8% p.a is ___________
The time taken for ₹ 1000 to become ₹ 1331 at 20% p.a, compounded annually is 3 years
Find the compound interest for `2 1/2` years on ₹ 4000 at 10% p.a, if the interest is compounded yearly
The number of conversion periods in a year, if the interest on a principal is compounded every two months is ___________
The sum which amounts to ₹ 2662 at 10% p.a in 3 years, compounded yearly is _________
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 ______.
