Question
In: Finance
You just turned 30 and decide that you would like to save up enough money so...
You just turned 30 and decide that you would like to save up
enough money so as to be able to withdraw $75,000 per
year for 20 years after you retire at age 65, with the first
withdrawal starting on your 66th birthday. How much money
will you have to deposit each month into an account earning
8% per year (interest compounded monthly), starting one
month from today, to accomplish this goal?
If possible, I want to see full math work behind it instead of a calculator.
Solutions
Expert Solution
| Amount required for retirement income | P×[1-(1÷(1+r)^n)]÷r | |
| Here, | ||
| A | Interest rate per annum | 8.00% |
| B | Number of years | 20 |
| C | Number of compoundings per per annum | 1 |
| A÷C | Interest rate per period ( r) | 8.00% |
| B×C | Number of periods (n) | 20 |
| Payment per period (P) | $ 75,000 | |
| Amount required for retirement income | $ 736,361 | |
| 75000×(1-(1÷(1+8%)^20))÷8% |
| Deposit in each month (P) | FVA÷([(1+r)^n-1]÷r) | |
| Here, | ||
| A | Interest rate per annum | 8.00% |
| B | Number of years | 35 |
| C | Number of payments per per annum | 12 |
| A÷C | Interest rate per period ( r) | 0.67% |
| B×C | Number of periods (n) | 420 |
| Future value of annuity (FVA) | 736,361 | |
| Deposit in each month (P) | 321 | |
| 736361÷(((1+0.67%)^420-1)÷0.67%) |
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