Question 1203599

 The formula for an investment worth with interest compounded annually is 

{{{A=P(1+i)^n}}}

where{{{ P}}} represents the initial investment,{{{ i }}}is the interest rate, and {{{A }}}is the worth of the investment after {{{n}}} years.


a) Rearrange the formula for{{{ P}}}. What was the initial investment of an investment worth ${{{1000}}} that compounded {{{10}}}% interest for{{{ 10}}} years?

{{{A=P(1+i)^n}}}

{{{P=A/(1+i)^n}}}


if

{{{A=1000}}}
 {{{i=10}}}%={{{0.10}}}
{{{n=10}}}

{{{P=1000/(1+0.10)^10}}}

{{{P=385.54}}}


b) Rearrange the formula for{{{ i}}}. What is the interest rate of an investment whose worth went from ${{{1000}}} to ${{{1200}}} in {{{2 }}}years?


{{{A=P(1+i)^n}}}

{{{A/P=(1+i)^n}}}

{{{root(n,A/P)=1+i}}}

{{{ i=root(n,A/P)-1}}}


if

{{{P=1000 }}}
{{{A=1200}}}
{{{n =2}}} years


{{{ i=root(2,1200/1000)-1}}}

{{{ i=root(2,12/10)-1}}}

{{{ i=root(2,6/5)-1}}}

{{{ i=1.096-1}}}

{{{ i=0.095445}}}  or {{{i=9.5445}}}%


c) Explain a method with which you could estimate how many years it would take for an investment to reach a certain worth at a certain interest rate.


The Rule of {{{72}}} is a calculation that estimates the number of years it takes to double your money at a specified rate of return. 

for example

 ${{{100}}} at {{{10}}}% will double to ${{{200 }}}in: {{{72/10=7.2}}} years


d) Estimate how many years would it take an investment of ${{{2100}}} at{{{ 20}}}% interest to reach a worth of ${{{5225}}}?


Note: We don't have to "estimate" but will solve it exactly!!!


to  reach a worth of ${{{5225 }}}will be

{{{5225=2100(1+0.20)^n}}}

{{{n}}}≈{{{4.9995 }}}

{{{n}}}≈{{{5 }}}years