Question

Your daughter will start college one year from today, at which time the first tuition payment of \$58,000$58,000 must be made. Assume that tuition does not increase over time and that your daughter remains in school for four years. How much money do you need today in your savings account, earning 5\%5% per annum, in order to make the tuition payments over the next four years, provided that you have to pay 35\%35% per annum in taxes on any earnings (e.g., interest on the savings)?

Answer 1

Answer:

Answer: I'll need $2,14,309.02 in my savings account in order to make tuition payments over the next four years.

We follow these steps in order to arrive at the answer:

In this question, we need to take into account that we need to pay 35% as taxes on interest earned.

So even though the interest rate on the deposit is 5%, only will be available for use.

Hence, effectively the deposit will only earn \begin{lgathered}0.05*0.65 = 0.0325\\\end{lgathered}

0.05∗0.65=0.0325

or 3.25% interest after taxes.

We'll compute the the Present Value of the annuity of 58,000 for four years at 3.25% interest in order to determine the amount that is needed today.

The Present Value of an Annuity formula is

\mathbf{PV_{Annuity}= PMT\left ( \frac{1 -(1+r)^{-n}}{r} \right )}PV

Annuity

=PMT( r

1−(1+r)

−n)

Substituting the values in the equation above we get,

PV_{Annuity}= 58,000\left (\frac{1 -(1.0325)^{-4}}{0.0325} \right )PV

Annuity

=58,000(0.0325

1−(1.0325)

−4)

PV_{Annuity}= 58,000\left (\frac{ 0.12008695 }{0.0325} \right )PV

Annuity

=58,000( 0.0325

0.12008695)

I hope this will help you

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Answer 2

The money needed today in the savings account is $2,14, 309.02.

Given:

The tuition fee for 1 year, A = $58,000.

The deposit interest rate = 5% per annum.

The tax imposed on earnings = 35% per annum.

The number of years, n = 4.

To Find:

We have to find the money needed today in the savings account in order to make the tuition payments over the next four years, after paying taxes.

Solution:

The effective interest rate (i) is calculated using the equation,

The effective interest rate (i) = Deposit interest rate × Interest earned

On substituting the given values in above equation, we get,

$i$ = 5% × (1 - 35%) = $\frac{5}{100}$ × $(1 - \frac{35}{100} )$ $= 0.0325$.

The money needed today in the savings account or present value (PV) is calculated using the below equation.

$PV = A$ × $(\frac{1-(1+i)^{n} }{i} )$

Substituting the given values, the above equation becomes,

$PV = 58,000$ × $(\frac{1-(1+0.0325)^{4} }{0.0325} )$

On simplifying, we get the above equation as,

$PV = 58,000$ × $3.69 =2,14, 309.02$ .

∴, The present value = $2,14, 309.02.

Hence, the money needed today in the savings account in order to make the tuition payments over the next four years, after paying taxes is $2,14, 309.02.

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