A carpenter's apprentice wishes to save enough money for his retirement at 65. If he is 25 now and can only afford to deposit $5,000 in his retirement account every second year, and expects an average annual return of 8% compounded annually, how much would he have saved in his account when he retires at 65? Thanks for help.
+36923 Hi guest.....I cannot seem to get this same answer.....I assumed he would put 5000 in NOW (beginning of year 1) and then 19 more times until he was 63....this amount would earn interest for two more years and then he would make his final 5000 payment (which would not earn interest)
Are these your assumptions? Or did you wait two years before he made a deposit? Did he make deposits at BEGINNING of years or END of the years ?
Thanx ! Just trying to reconcile may calcs (my answer is higher than yours)
There are a couple of ways of approaching this problem:
1) Because the payments are made every 2nd year, will assume that they are deposited at the END of the year, it is always easiest to make the interest rate MATCH the deposits. Since the interest rate is 8% compounded annually, will simply compound it for two years. So, we have: 1.08^2 =1.1664 -1 x 100 =16.64%. Now, will use the common formula for FV of $1 per period, or:
FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD.
FV =5,000 x [1 + 0.1664]^20 - 1 / 0.1664
FV =5,000 x 124.5464
FV =$622,732.02 - which is what he would expect to have in his retirement account.
2) The 2nd approach is find the equivalent ANNUAL payments, using the exact same formula above and solve for payments as follows:
5,000 = P x 1.08^2 - 1 / 0.08
5,000 =P x 0.1664 / 0.08
5,000 =P x 2.08
P =2,403.85 equivalent annual payments. Then, we use the above formula for 40 years.
FV =2,403.85 x [1.08]^40 - 1 /0.08
FV =$622,733.02, which is the same as above. $1's difference is due to rounding off the annual payments.
+36923 Those are the equations I was using...With the following assumptions (since the question is a bit ambiguous)
Assumingpt he puts in his first 5000 NOW and then every other year for 19 more deposits the result is significantly higher:
726,354.62 vs 622,732.02 (essentially two more years of compound int added to this amount) AND if he puts in 5000 on his 65th it would be 731,354.62 !
Moral of the story: Start NOW or as soon as you can with your retirement savings/planning !!!!!! LOL
