Finding Time Period of Investment

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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