Question

Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.):

Present Value	Years	Interest Rate %		Future Value
$600		8		1,393
$850		12		2,330
$18,800		18		367,247
$21,900		14		382,893

Answer 1

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A= P ( 1+ r/100) ^ n

1,393= 600*(1+8/100) ^n

or 1,393 / 600 = (1+8/100) ^n

or 2.3216666667 = (1.08) ^ n

Taking log on both sides we get,

log 2.3216666667 = n log (1.08)

Hence, n = Log 2.3216666667 / log (1.08)

or n = 10.94430774 Years

Hence the correct answer is 10.94 Years

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We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A= P ( 1+ r/100) ^ n

2330 = 850 *(1+12/100) ^n

or 2330 / 850 = (1+12/100) ^n

or 2.741176471 = (1.12) ^ n

Taking log on both sides we get,

log 2.741176471= n log (1.12)

Hence, n = Log 2.741176471 / log (1.12)

or n =8.897899012 Years

Hence the correct answer is 8.90 Years

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We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

$ 367,247 = $18,800 * ( 1+18/100) ^ n

$ 367,247 / $18,800 = 1.18 ^ n

or 19.53441489= (1.18) ^ n

Taking log on both sides we get,

log 19.53441489= n log (1.18)

Hence, n = Log 19.53441489/ log (1.18)

or n = 17.95721149 Years

Hence the correct answer is 17.96 Years

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We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

$ 382,893 = $ 21,900 * ( 1+14/100) ^ n

$ 382,893 / $ 21,900 = 1.14 ^ n

or 17.48369863= (1.14) ^ n

Taking log on both sides we get,

log 17.48369863= n log (1.14)

Hence, n = Log 17.48369863/ log (1.14)

or n= 21.83703643 Years

Hence the correct answer is 21.84 Years