Question

**PLEASE USE yn=(b/1-a)+(yo-b/1-a)(a^n)

a. Sharon wants to retire in 30 years time, and so decides to start a new retirement savings account. She wants to accumulate 250000 dollars by the time she retires. Initially, Sharon deposits 2000 dollars into the account. She will make further deposits at the end of each month. The account will earn interest at annual rate 8 percent, compounded monthly. How much will she have to deposit into the account each month in order to reach this target after 30 years? (Give your answer, in dollars, correct to the nearest cent.) monthly deposit _______

b. Derek has just retired, and has 750000 dollars in his retirement account. The account will earn interest at an annual rate of 5 percent, compounded monthly. At the end of each month, Derek will withdraw a fixed amount to cover his living expenses. Derek wants his savings to last exactly 25 years. How much money can he withdraw each month? (Give your answer in dollars, correct to the nearest cent.)

monthly withdrawal: ________

What is the maximum amount that Derek can withdraw each month if he wants his savings to last indefinitely?

monthly withdrawal: _________

Answer 1

Hi

FV of initial deposit = 2000(1+0.05/12)^360 = $4467.74*2=$8935.48

balance FV needed = $250,000 - $8935.48 = $241064.52

PMT((1 +0.05/12)^360 - 1)/(0.05/12) = 832.258635*PMT

PMT =241064.52/832.258635 = $289.650968896225 ≈ $290.00

2.

Derek has $750000

Earn interest compounded monthly @5%

So now

A = $750000 * (1 + 0.06/12)^(12 * 1/6)

≈ $757518.75≈$757519.00

Say that the money doesn't spent in 25 years so

=$757519.00/12*25

=$2525.06333333333≈$2525.00

He have to withdraw $2525.00 per month to last his money for 25years