Question

ccepi My courses > 3001 > Homework NU. 4 Intro You just turned 25 years old and want to retire when you turn 65. You plan to put $4,600 every year into a ROTH IRA, a retirement account from which you can withdraw money after retirement without having to pay any taxes. You expect to earn a return of 6% on your investments every year. Part 1 - Attempt 1/10 for 10 pts. How much money can you expect to have at age 65 if you make your first annual deposit now and your last one on the day you turn 64? No decimals Submit IB Part 2 Attempt 1/10 for 10 pts. How much money can you expect to have at age 65 if you make your first deposit 10 years from now (at age 35) and your last one on the day you turn 647 No decimals

Answer 1

Part 1

The formula to calculate accumulated value is given below:

Accumulated value = Cash flow x ((1+i)-1) (1 - (1 + i)-1)

$Accumulated\, value=4,600\times \left ( \frac{\left ( 1+0.06 \right )^{40}-1}{1-\left ( 1+0.06 \right )^{-1}} \right )$

Accumulated value = 4, 600 x 9.285718 0.05660377)

$Accumulated\, value=4,600\times 164.0476$

Part 2

There will be total 30 deposits.

$Accumulated\, value=4,600\times \left ( \frac{\left ( 1+0.06 \right )^{30}-1}{1-\left ( 1+0.06 \right )^{-1}} \right )$

$Accumulated\, value=4,600\times \left ( \frac{4.743491}{0.05660377} \right )$

$Accumulated\, value=4,600\times 83.8016774$