A young married couple intends to save some money for their retirement at age 65. They began their retirement plan by depositing a fixed amount of money annually for 5 years, and they would skip the next 5 years. They would continue with this scheme for 40 years. In other words, 5 years on and 5 years off. If they intend to save $500,000 and can earn 5% compounded annually, how much money do they expect to deposit each active year until their retirement at 65?. Thank you for any help.
A problem, such as this, requires a multi-step solution.
First, find the FV of $1 per period for the first 5 years @ 5% using this common formula: FV =$1 x (1.05^5 - 1) / 0.05=$5.53. Then project this amount forward for the second 5-year period using this second common FV formula: FV = PV x 1.05^5 =$5.53 x 1.2762815625=$7.05. Then continue this process for eight 5-year periods. You should get the following amounts:
At the end of the first 5-year period =$5.53
At the end of the second 5-year period=$7.05
At the end of the third 5-year period =$14.53
At the end of the fourth 5-year period=$18.54
At the end of the fifth 5-year period =$29.19
At the end of the sixth 5-year period=$37.25
At the end of the seventh 5-year period=$53.07
At the end of the eighth 5-year period =$67.73
This last amount shown to 10 decimal places=$67.7308673760.
Since the young couple's wish is to have $500,000 at 65, then we just divide: $500,000 / $67.7308673760 =$7,382.16 - which is their expected annual payment into their retirement fund.