Page 202 - Start Up Mathematics_8 (Non CCE)

Example 8: Find the amount on ` 15,625 in 9 months at the rate of 6% per annum, when the interest is
compounded quarterly.
9 3
Solution: P = ` 15,625, R = 16% per annum, n = 9 months = years = years
12 4
3
3 Ê R ˆ 4n Ê 16 ˆ 4 ¥ 4
Amount after years = P 1+ ˜ = ` 15,625 1+ ˜
Á
Á
4 Ë 400¯ Ë 400¯
1 ˆ
Ê
= ` 15,625 1+ 25¯ ˜ 3 = ` 15,625 Ê Á Ë 26ˆ 3
˜
Á
Ë
25¯
Ê
= ` 15 625, ¥ 26 ¥ 26 ¥ 26ˆ = ` 17,576
Á
˜
25¯
Ë
25
25
Example 9: Manav took a loan of ` 3,90,625 from a private financer. If the financer charges interest at the
rate of 16% per annum, compounded quarterly. What amount will discharge Manav’s debt after
1 year? Also find the compound interest on the principal.
Solution: P = ` 3,90,625, R = 16% per annum, n = 1 year
Ê R ˆ 4n Ê 16 ˆ 41¥
\ Amount after 1 year = P 1+ 400¯ ˜ = ` 3,90,625 1+ 400¯ ˜
Á
Á
Ë
Ë
Ê 1 ˆ 4 Ê 26ˆ 4
= ` 3,90,625 1+ 25¯ ˜ = ` 3,90,625 × Á Ë 25¯ ˜
Á
Ë
Ê 26 26 26 26ˆ
= ` 390 625, , ¥ 25 ¥ 25 ¥ 25 ¥ 25¯ ˜ = ` 4,56,976
Á
Ë
An amount of ` 4,56,976 will discharge Manav from his debt after 1 year.
\ C.I. = A – P = ` (4,56,976 – 3,90,625) = ` 66,351
Computation of compound interest when the interest is compounded annually but the rates are different for
different years
If, P = Principal
R %, R %, R %, ......, R % = rates of interest for 1st, 2nd, 3rd, ......, nth year respectively
n
3
2
1
Ê R ˆ Ê R ˆ Ê R ˆ Ê R ˆ
A = P 1+ 100¯ Ë 1+ 100¯ Ë 1+ 100¯ ˜ ...... 1+ 100¯ then C.I. = A – P
3
2
n
1
Á
˜ Á
˜
Á
˜ Á
Ë
Ë
Example 10: Find the amount and compound interest on ` 6,000 in 3 years if the rate of interest is 5% for
the first year, 4% for the second year and 3% for the third year.
Solution: P = ` 6,000, R = 5% per annum, R = 4% per annum, R = 3% per annum
1
3
2
Ê R ˆ Ê R ˆ Ê R ˆ
Amount after 3 years = P 1+ 100¯ Ë 1+ 100¯ Ë 1+ 100¯
3
2
1
˜ Á
˜
Á
˜ Á
Ë
Ê 5 ˆ Ê 4 ˆ Ê 3 ˆ
= ` 6,000 1+ 100¯ Ë 1+ 100¯ Ë 1+ 100¯
˜
˜ Á
Á
˜ Á
Ë
Ê 1 ˆ Ê 1 ˆ Ê 3 ˆ 21 26 103
= ` 6,000 1+ 20¯ Ë 1+ 25¯ Ë 1+ 100¯ = ` 6,000 × 20 × 25 × 100
Á
˜
˜ Á
˜ Á
Ë
= ` 6,748.56
\ C.I. = A – P = ` (6,748.56 – 6,000) = ` 748.56
194