Question

Investing. How many years will it take $9,000 to grow to $16,700 if it is invested at 3% ​(A) compounded​ quarterly? ​(B) compounded​ continuously?

Answer 1

A) Future Value = Present Value * (1+Rate of Interest)^Time

16,700 = 9000 * (1+3%/4) ^Time

16,700 / 9,000 = 1.0075 ^Time

Let time be n years

Taking log on both sides,

log ( 16700/9000) = n log(1.0075)

n =  log ( 16700/9000) / log(1.0075)

= 82.73 quarters

Time = 82.73/4

= 20.68 years

Answer = 20.68 Years

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B)Future Value = Present Value * e^rt

where e is 2.71828

rate = 3%

Let time = n  

16700 = 9000 * 2.71828^(0.03n)

16700/9000= 2.71828^(0.03n)

Taking log on both sides:

log (16700/9000)= 0.03 n * log 2.71828

n= 1/0.03 [ log (16700/9000) / log 2.71828]

n = 20.61 Years

Answer = 20.61 Years