coexpennan

2021-08-18

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 $3\mathrm{%}$.

Calculation:
Write the expression for future value.
$F=A\frac{\left({\left(1+i\right)}^{n}-1\right)}{i}$ .......(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 $7.3\mathrm{%}$.
Substitute $2000000 for F and 0.073 for i and 30 for n in Equation (I). $\mathrm{}2000000=A\frac{\left({\left(1+0.073\right)}^{30}-1\right)}{0.073}$ $A=\frac{\mathrm{}2000000}{99.72}$ $A=\mathrm{}20056$ Conclusion: Thus, the amount of money invested each year is$20056.
Calculation:
Calculate the amount contributed each year by the employer.
${A}_{E}=\mathrm{}65000×3\mathrm{%}$
$=\mathrm{}65000×0.03$
$=\mathrm{}1950$
Calculate the amount invested by the employer.
${A}_{\mathrm{\exists }}=A-{A}_{E}$ .......(II)
Here, the annual amount to be invested is A, the annual amount invested by the employer is ${A}_{E}$ and the annual amount invested by the employee is ${A}_{\mathrm{\exists }}$.
Substitute $20056 for A,$1950 for ${A}_{E}$ in Equation (II).
${A}_{\mathrm{\exists }}=\mathrm{}20056-\mathrm{}1950$
$=\mathrm{}18106$
Conclusion:
Thus, the amount invested by the employer annually is $1950. The amount invested by the employee annually is$18106.

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