Please help!
After realizing that social security may not exist by the time you retire, you decide it is time to get to work on retirement saving. As an college graduate you will make $45,000 next year before taxes. You expect this salary to grow at 4.5 percent annually until you retire in 40 years. In retirement you believe you will need 65 percent of your final pre-retirement salary to live comfortably. This amount will need to grow at 2 percent annually to keep up with inflation (the first inflation adjustment will occur the year you retire). Due to rising life expectancies, you believe you will need your income in retirement to last 30 years. You will spend your last dollar on the day you die. Funds that you save can be invested in a mutual fund earning 7 percent annually. (Assume all cash flows occur at the end of the year.)
What percent of your salary do you need to invest annually to live comfortably in retirement? (Assume that you invest the same percent every year.)
So far I got the following:
65% of last earning is $162,802.55
Total adjusted first year with inflation for 30 years: $6,736,678.40
Discounted: $2,530,887.98
I know the answer is 15.35% but I'm having difficulty reaching it.
I'm using the solver function in the calculator which is shown as follows:
N= 40
I%= 7
PV= 0
PMT= 0
FV = 2530887.98
And the payment I get is about 4% of my total salary ($4816364.54)
The payment I get is 12677.57
After realizing that social security may not exist by the time you retire, you decide it is time to get to work on retirement saving. As an college graduate you will make $45,000 next year before taxes. You expect this salary to grow at 4.5 percent annually until you retire in 40 years. In retirement you believe you will need 65 percent of your final pre-retirement salary to live comfortably. This amount will need to grow at 2 percent annually to keep up with inflation (the first inflation adjustment will occur the year you retire). Due to rising life expectancies, you believe you will need your income in retirement to last 30 years. You will spend your last dollar on the day you die. Funds that you save can be invested in a mutual fund earning 7 percent annually. (Assume all cash flows occur at the end of the year.)
What percent of your salary do you need to invest annually to live comfortably in retirement? (Assume that you invest the same percent every year.)
So far I got the following:
65% of last earning is $162,802.55
Total adjusted first year with inflation for 30 years: $6,736,678.40
Discounted: $2,530,887.98
I know the answer is 15.35% but I'm having difficulty reaching it.
I'm using the solver function in the calculator which is shown as follows:
N= 40
I%= 7
PV= 0
PMT= 0
FV = 2530887.98
And the payment I get is about 4% of my total salary ($4816364.54)
The payment I get is 12677.57