Finding Time Period of Investment
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For finding time period of investment we use the same formula of amount.A = P ( 1 + r )^{n}
Where, P = Principal
R = rate in percent
n = time in years
Examples :
1) Finding time period of investment when $ 800 amount to $882 at 5 % p.a. compounded annually ?
Solution :
Here, P = $ 800 , A = $ 882 , r = 5 % = 0.05
A = P( 1 + r) ^{n}
882 = 800 ( 1 + 0.05) ^{n}
882 = 800 ( 1.05) ^{n}
882/800 = ( 1.05) ^{n}
882 105 ------- = --------- 800 100 |
441 21 ------- = --------- 400 20 |
(21)^{2} (21)^{n} ------- = --------- (20)^{2} (20)^{n} |
∴ n = 2
Hence, time period is 2 years.
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2) In what time will $ 64,000 amount to $ 68,921 at 5% p.a. interest being compounded half yearly?
Solution :
Here, P = $ 64,000 ; A = $ 68,921 and rate = 5 % = 0.05
As the interest is being compounded half yearly so
A = P ( 1 + r/2) ^{2n}
⇒ 68921 = 64000( 1 + 0.05/2) ^{2n}
⇒ 68921 = 64000(1 + 0.025) ^{2n}
⇒ 68921 = 64000 ( 1.025) ^{2n}
⇒ 68921/64000 = ( 1025/1000) ^{2n}
⇒ ( 41/40) ^{3} = (41/40) ^{2n}
As the bases are same so the exponents are equal.
∴ 2n = 3
n = 3/2 years.
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3) Finding the time period of investment when $4400 will amount to $4576 at 8% per annum, if interest is compounded half yearly.
Solution :
Here, P = $ 4400 , A = $ 4576 ,
r = 8 %
&ther4; For half yearly, r = 4%
A = P( 1 + r) ^{n}
4576 = 4400 ( 1 + 0.04) ^{n}
4576 = 4400 ( 1.04) ^{n}
4576/4400 = ( 1.04) ^{n}
4576 (104)^{n} ⇒ ------- = --------- 4400 (100)^{n} |
4576 (26)^{n} ------- = --------- 4400 (25)^{n} |
After writing the fraction 4576/4400 in lowest form we get 26/25
(26) (26)^{n} ------- = --------- (25) (25)^{n} |
∴ n = 1
Hence, time period is 1 years.
Compound Interest ( CI )
• Find Compound Interest when interest is compounded Half yearly
• Find Compound Interest when interest is compounded Quarterly
• Find CI when interest is compounded annually but Rates are different
• Finding Principal
• Finding Time Period of Investment
• Finding Rate of Interest
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