Question

If Tanisha has $1,000 to invest at 6% per annum compounded semiannually, how long will it be before she has $1,350? If the compounding is continuous how long will it be

Answer 1

The Time period for investment at 6 % semiannually is 27 years

Explanation:

Given as :

The principal investment = $ 1000

The rate of interest = 6% compounded semiannually

The Amount after T year = $ 1350

Let the time period = T year

Now, From compounded method

Amount = Principal ×
`(1+(\textrm Rate)/(6* 100))^(\textrm time* 6)`

or, $ 1350 = $1000 ×
`(1+(\textrm 6)/(6* 100))^(\textrm T* 6)`

Or,
`(1350)/(1000)` =
`(1.01)^(T)`

Or, 1.35 =
`(1.01)^(T)`

or,
`(1.31)^{(1)/(T)}` = 1.01

Now Taking log both side

Log
`(1.31)^{(1)/(T)}[/tex = Log 1.01</p><p>Or, [tex](1)/(T)` × 0.11727 = 0.0043213

So, T =
`(0.11727)/(0.0043213)`

∴ T = 27.11 ≈ 27 years

Hence The Time period for investment at 6 % semiannually is 27 years . Answer