Question 1204380

A newscaster earns ${{{26100}}} => assuming this is annual salary
wants to invest {{{10}}}% of his/her {{{monthly}}} salary to save for retirement in {{{38}}} years

 
If he/she invests this money at{{{ 5.1}}}% compounded monthly, how much money will he/she have at retirement?




a) How much will be saved each year?

we first need to calculate  {{{10}}}% ={{{0.1}}} of ${{{26100}}}:

Annual savings = ${{{26100 * 0.1}}}

Annual savings = ${{{2610}}}

So, the newscaster will save ${{{2610}}} each year.


What will be the amount in the account after {{{38 }}}years?


To find the amount in the account after {{{38 }}}years, we will use the formula:

{{{FV = P *((1 + r)^(nt) - 1) / r}}}

Where {{{FV }}}is the future value, {{{P }}}is the {{{monthly}}} deposit,{{{ r }}}is the monthly interest rate (annual interest rate divided by {{{12}}}), {{{n}}} is the number of times interest is compounded per year (monthly, so {{{12}}}), and {{{t}}} is the number of years.


 find the monthly deposit, we need to divide the annual savings by the number of months in a year:


Monthly deposit ={{{ 2610 / 12}}}

Monthly deposit {{{P = 217.5}}}


so, we have:

 {{{P = 217.5}}} 

convert {{{5.1}}}% to decimal:{{{0.051}}}

{{{r = 0.051/12=0.00425}}}

{{{n = 12}}} months

{{{t = 38}}} years



Now, plug the values into the formula:

{{{FV = 217.5 *((1 + 0.00425)^(12*38) - 1) /(0.00425)}}}

{{{FV =302779.76}}}