Respuesta :
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 [tex]1 - 35% = 65%[/tex] will be available for use.
Hence, effectively the deposit will only earn [tex]0.05*0.65 = 0.0325\\[/tex] 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
[tex]\mathbf{PV_{Annuity}= PMT\left ( \frac{1 -(1+r)^{-n}}{r} \right )}[/tex]
Substituting the values in the equation above we get,
[tex]PV_{Annuity}= 58,000\left (\frac{1 -(1.0325)^{-4}}{0.0325} \right )[/tex]
[tex]PV_{Annuity}= 58,000\left (\frac{ 0.12008695 }{0.0325} \right )[/tex]
[tex]\mathbf{PV_{Annuity}= 58,000 * 3.69 = 2,14,309.02}[/tex]
The Pearson will need $2,14,309.02 in his savings account in order to make tuition payments over the next 4 years, this is computed by the present value of the annuity.
What is the present value of annuity?
The present value of a sum of money, as opposed to the future worth of it, will have when compound interest has been applied.
Computation:
According to the given information, interest earned is taxed at a rate of 35%.
Even though the deposit has a 5% interest rate, only a portion of it will be available for usage.
Hence, effectively the deposit will be:
[tex]\text{Effective Rate of Interest}=\text{Deposit Interest Rate}\times \text{Interest earned}\\\\\text{Effective Rate of Interest}=5\% \times (1 - 35\%)\\\\\text{Effective Rate of Interest}= 0.0325\\[/tex]
It is given that the Annuity is $58,000.
To estimate the amount required present, compute the Present Value for four years at 3.25 % or 0.0325.
Now, put the values in the formula of Present Value (PV) of an Annuity is:
[tex]\text{PV} = \text{A}( \dfrac{1-(1+i)^n}{i})\\\\\text{PV} =\$58,000( \dfrac{1-(1+0.0325)^4}{0.0325})\\\\\text{PV} =\$58,000 \times 3.69\\\\\text{PV} =\$2,14,309.02[/tex]
Therefore, $2,14,309.02 is the present value of the tuition fees.
Learn more about the Present value, refer to:
https://brainly.com/question/17322936
