a) The amount of money invested each year.Given: Annual incone is $65000.Number of year is 30.Future Value is $2000000.b) The amount of money each should invest annualy.Saving is 3\%.

coexpennan 2021-08-18 Answered
a) The amount of money invested each year.
Given: Annual incone is $65000.
Number of year is 30.
Future Value is $2000000.
b) The amount of money each should invest annualy.
Saving is \(\displaystyle{3}\%\).

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Expert Answer

Sadie Eaton
Answered 2021-08-19 Author has 28373 answers
Calculation:
Write the expression for future value.
\(\displaystyle{F}={A}{\frac{{{\left({\left({1}+{i}\right)}^{{{n}}}-{1}\right)}}}{{{i}}}}\) .......(I)
Here, the future value is F, the annual investment is A, the interest rate is i and the number of period is n.
The interest rate for stock fund is \(\displaystyle{7.3}\%\).
Substitute $2000000 for F and 0.073 for i and 30 for n in Equation (I).
\(\displaystyle\${2000000}={A}{\frac{{{\left({\left({1}+{0.073}\right)}^{{{30}}}-{1}\right)}}}{{{0.073}}}}\)
\(\displaystyle{A}={\frac{{\${2000000}}}{{{99.72}}}}\)
\(\displaystyle{A}=\${20056}\)
Conclusion:
Thus, the amount of money invested each year is $20056.
Calculation:
Calculate the amount contributed each year by the employer.
\(\displaystyle{A}_{{{E}}}=\${65000}\times{3}\%\)
\(\displaystyle=\${65000}\times{0.03}\)
\(\displaystyle=\${1950}\)
Calculate the amount invested by the employer.
\(\displaystyle{A}_{{\exists}}={A}-{A}_{{{E}}}\) .......(II)
Here, the annual amount to be invested is A, the annual amount invested by the employer is \(\displaystyle{A}_{{{E}}}\) and the annual amount invested by the employee is \(\displaystyle{A}_{{\exists}}\).
Substitute $20056 for A, $1950 for \(\displaystyle{A}_{{{E}}}\) in Equation (II).
\(\displaystyle{A}_{{\exists}}=\${20056}-\${1950}\)
\(\displaystyle=\${18106}\)
Conclusion:
Thus, the amount invested by the employer annually is $1950.
The amount invested by the employee annually is $18106.
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