Advertisements
Advertisements
Question
Find the difference between the compound interest compounded yearly and half-yearly on Rs. 10,000 for 18 months at 10% per annum.
Advertisements
Solution
Given: P = Rs. 10,000 ; n = 18 months = `1 1/2` year and r = 10% p.a.
For First year
I = `(10,000xx10xx1)/100`
= 1,000
A = 10,000 + 1,000
= 11,000
For Second year,
P = 11,000, r = 10%, n = `1/2` year
I = `(11,000xx10xx1/2)/100`
= 550
A2 = 11,000 + 550
= 11,550
C.I. = A – P
= 11,550 – 10,000
= 1,550
When interest is compounded half-yearly
`A = P (1 + r/200)^(nxx2)`
= `10,000 (1 + 10/200)^(3/cancel2 xxcancel2`
=`10,000 xx 21/20 xx 21/20 xx 21/20`
= `(105 xx 441)/4`
= `46305/4`
= 11576.25
Compound interest yearly = 11576.25 – 10,000
= 1576.25
Therefore, the difference between both C.I
= 1576.25 – 1,550
= 26.25
APPEARS IN
RELATED QUESTIONS
What sum of money will amount to Rs. 27,783 in one and a half years at 10% per annum compounded half yearly?
At what rate of interest per annum will a sum of Rs. 62,500 earn a compound interest of Rs. 5,100 in one year? The interest is to be compounded half yearly.
Calculate the C.I. on Rs. 3,500 at 6% per annum for 3 years, the interest being compounded half-yearly.
Do not use mathematical tables. Use the necessary information from the following:
(1.06)3 = 1.191016; (1.03)3 = 1.092727
(1.06)6 =1.418519; (1.03)6 = 1.194052
Find the difference between compound interest and simple interest on Rs.12,000 and in `1 1/2` years at 10% compounded yearly.
Find the difference between compound interest and simple interest on Rs. 12,000 and in `1 1/2` years at 10% compounded half-yearly.
Find the amount and the compound interest payable annually on the following :
Rs.24000 for 1`(1)/(2)` years at 7`(1)/(2)`% per annum.
[Hint : 1 year 146 days = `1(146)/(365)"year" = 1(2)/(5)"year"`]
A man lends Rs 15000 at 10.5% per annum C.I., interest reckoned yearly, and another man lends the same sum at 10% per annum, interest being reckoned half-yearly. Who is the gainer at the end of one year and by how much?
Find the amount and the compound interest on the following :
Rs.15000 for 2years at 8% per annum compounded semi-annually.
Find the amount and the compound interest on the following :
Rs.25000 for 2 years at 6% per annum compounded semi-annually.
Find the amount and compound interest on Rs.50000 on 1`(1)/(2)` years at 8% p.a. compounded half-yearly.
