gary has just retired, and has 750000 dollars in his retirement account. the account will earn interest at an annual rate of 5 p

Question

1 year ago

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gary has just retired, and has 750000 dollars in his retirement account. the account will earn interest at an annual rate of 5 p

ercent, compounded monthly. at the end of each month, gary will withdraw a fixed amount to cover his living expenses. gary wants his savings to last 30 years. how much money can he withdraw each month

Mathematics

1 answer:

ch4aika [34] · Answer 1 · 2024-09-10T23:43:30+03:00

The amount of money that Gary can withdraw each month is equal to $4026.18.

<u>Given the following data:</u>

Value of each payment, P = 750,000 dollars.

Annual percentage interest rate, APR = 5% = 0.05.

Time, t = 30 years.

APR is an acronym for annual percentage rate and it can be defined as a measure of an amount of money based on a yearly rate of interest, which a borrower must pay on a loan or credit card.

This ultimately implies that, the annual percentage rate (APR) would be calculated by dividing the rate of interest by twelve (12).

Rate of interest, r = APR/12

Rate of interest, r = 0.05/12

Rate of interest, r = 0.0041667

Next, we would calculate the present value of this ordinary annuity by using this formula:

Present value, PV = [P ÷ [1 - (1 + r)^{-nt}]/r]

Substituting the given parameters into the formula, we have;

Present value = [750,000 ÷ [(1 - (1 + 0.0041667)^{-30 × 12})/0.0041667]

Present value = [750,000 ÷ [(1 - (1.0041667)^{-360})/0.0041667]

Present value = [750,000 ÷ [(1 - 0.2238239)/0.0041667]

Present value = [750,000 ÷ [0.7761761/0.0041667]

Present value = 750,000 ÷ 186.280773754