Mathematics: 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

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If tanisha has $1,000 to invest at 6% per annum compounded

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Liapis

10.01.2022

Mathematics

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

Step-by-step 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 × $(1+\dfrac{\textrm Rate}{6\times 100})^{\textrm time\times 6}$

or, $ 1350 = $1000 × $(1+\dfrac{\textrm 6}{6\times 100})^{\textrm T\times 6}$

Or, $\frac{1350}{1000}$ = $(1.01)^{T}$

Or, 1.35 = $(1.01)^{T}$

or, $(1.31)^{\frac{1}{T}}$ = 1.01

Now Taking log both side

Log $(1.31)^{\frac{1}{T}}[/tex = Log 1.01Or, [tex]\frac{1}{T}$ × 0.11727 = 0.0043213

So, T = $\frac{0.11727}{0.0043213}$

∴ T = 27.11 ≈ 27 years

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

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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

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