The annuity could provide $221.19 each month
Step-by-step explanation:
The ANNUITY FORMULA is [tex]P_{t}=\frac{d[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}[/tex] , where
1. [tex]P_{t}[/tex] is the balance in the account after t years
2. d is the regular deposit (the amount you deposit each year or month
or .........)
3. r is the annual interest rate in decimal
4. n is the number of compounding periods in one year
5. t the number of years
∵ Loren knows that he will have $500,000 when he retires
∴ [tex]P_{t}[/tex] = $500,000
∵ he sets up a payout annuity for 30 years in an account paying 10%
interest
∴ t = 30 years
∴ r = (10/100) = 0.1
∵ The annuity could provide each month
∴ n = 12
Substitute the values above in the formula
∴ [tex]500,000=\frac{d[(1+\frac{0.1}{12})^{(12)(30)}-1]}{\frac{0.1}{12}}[/tex]
∴ [tex]500,000=\frac{d[(1.00833333)^{360}-1]}{0.00833333}[/tex]
∴ 500,000 = d [2260.487925]
- Divide both sides by 2260.487925
∴ d = $221.19
The annuity could provide $221.19 each month
Learn more:
You can learn more about deposit in brainly.com/question/8782252
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