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
As the bases are same so the exponents are equal
∴ 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
As the bases are same so the exponents are equal
∴ 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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