Respuesta :
The amount that parent should deposit so that their son can receive monthly allowance of $600 is $7098.27.
Further Explanation:
The present value of an annuity is the value of future payments at the current, at a given rate of discount. The present value is calculated as:
[tex]${\text{PV=PMT\times}}\left({\frac{{\left({{\text{1}}-\left({\frac{{\text{1}}}{{{{{\text{(1 + r)}}}^{\text{n}}}}}}\right)}\right)}}{{\text{r}}}}\right)$[/tex]
Where,
PV = the present value of an annuity stream
PMT = the annual future payment
r = the interest rate or the discount rate
n = the number of periods
Calculate the present value of an annuity:
[tex]\begin{aligned}PMT&=\$600\\r&=6.65\%\\n&=2\times12\\&=24\\\end{aligned}[/tex]
And,
[tex]\begin{aligned}\text{PV}&=\text{PMT}\times\left[\dfrac{1-\left(\dfrac{1}{(1+r)^{n}}\right)}{r}\right]\\&=\$600\times\left[\dfrac{1-\left(\dfrac{1}{(1+0.0665)^{24}}\right)}{0.0665}\right]\\&=\$7098.27\end{aligned}[/tex]
The amount that parent should deposit so that their son can receive monthly allowance of $600 is $7098.27
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Answer details:
Grade: High School
Subject: Financial management
Chapter: Time value of money
Keywords:Parents want to setup an account for their child, studying abroad for next 2 years, w they can receive a monthly allowance of $600, the account will be compounded 6.65% monthly, amount should they deposit so their child could have the allowance, present value, of, the, investment, future value.
