Question

Parents want to setup an account for their child studying abroad for next 2 years, where they can receive a monthly allowance of $600. the account will be compounded 6.65% monthly. how much should they deposit so their child could have the allowance?

Answer 1

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:

${\text{PV=PMT\times}}\left({\frac{{\left({{\text{1}}-\left({\frac{{\text{1}}}{{{{{\text{(1 + r)}}}^{\text{n}}}}}}\right)}\right)}}{{\text{r}}}}\right)$

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:

$\begin{aligned}PMT&=\ 600\\r&=6.65\%\\n&=2\times12\\&=24\\\end{aligned}$

And,

$\begin{aligned}\text{PV}&=\text{PMT}\times\left[\dfrac{1-\left(\dfrac{1}{(1+r)^{n}}\right)}{r}\right]\\&=\ 600\times\left[\dfrac{1-\left(\dfrac{1}{(1+0.0665)^{24}}\right)}{0.0665}\right]\\&=\ 7098.27\end{aligned}$

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.

Answer 2

$639.90
Multiply $600 by .0665 which gives you $39.90, and then add $600 to that giving you $639.90