Mathematics, 08.08.2021 04:50 dylankrenek

Beth has just received an inheritance of $500,000 and would like to be able to make quarterly withdrawals over the next 20 years. She decides on an annuity that pays 6.4%, compounded quarterly. How much will her quarterly payments be to draw the account down to zero at the end of 20 years? Quarterly Payments =

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The amount Beth would be able to withdraw quarterly from her inheritance over the next 20 years is Quarterly Payments ≈ $11,124.53

The given parameters in the question;

Present value of inheritance, PV = $500,000

The number of years of withdrawal, n = 20 years

Interest rate, i = 6.4%

The required parameter;

The amount Beth would be able to withdraw quarterly over the next 20 years to draw the account down to zero, given a quarterly interest rate of 6.4%

Method

The required parameter is given by the payment formula

The question is related with annuity given that withdrawals will be made quarterly

The question seeks to find how much she can withdraw so as to exhaust the balance in 20 years

The amount she can withdraw quarterly is given by the payment formula as follows;

$\mathbf{PMT = PV \times \dfrac{i}{1 - \left(1 + i\right)^{-n}}}$

Where;

PMT = The amount of quarterly payments

PV = The present value of the investment = $500,000

i = The interest rate = 6.4%

n = The number of years = 20 years

Therefore, we get;

$\mathbf{PMT = 500,000 \times \dfrac{\dfrac{0.064}{4} }{1 - \left(1 + \dfrac{0.064}{4} \right)^{-4 \times 20}} \approx 11,124.53}$

The amount she can withdraw quarterly for the next 20 years ≈ $11,124.53

Quarterly payment, PMT = $11,124.53

Learn more about annuity here;

Answer from: Quest

step-by-step explanation:

5×5×5+2(8)÷2(2)+3(3)

15+16÷4+9

31÷13

do 31÷13 and u will get ur answer

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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