how much should you deposit at the end of each month in an ira that pays 5% compounded monthly to earn…

how much should you deposit at the end of each month in an ira that pays 5% compounded monthly to earn $110,000 per year from interest alone, while leaving the principal untouched, to be withdrawn at the end of each year after you retire in 40 years?\nclick the icon to view some finance formulas.\n\nthe monthly deposit is $□.\n(round up to the nearest dollar.)

how much should you deposit at the end of each month in an ira that pays 5% compounded monthly to earn $110,000 per year from interest alone, while leaving the principal untouched, to be withdrawn at the end of each year after you retire in 40 years?\nclick the icon to view some finance formulas.\n\nthe monthly deposit is $□.\n(round up to the nearest dollar.)

Answer

Explanation:

Step1: Find required principal $P$

We need annual interest of $110,000 at 5% annual rate. Use $I = P \times r$, so solve for $P$: $$P = \frac{I}{r} = \frac{110000}{0.05} = 2200000$$

Step2: Define annuity variables

For monthly compounding:

  • Annual rate $r = 0.05$, so monthly rate $i = \frac{0.05}{12}$
  • Number of periods $n = 40 \times 12 = 480$
  • Future value $FV = 2200000$

Step3: Solve for monthly deposit $PMT$

Use future value of ordinary annuity formula $FV = PMT \times \frac{(1+i)^n - 1}{i}$. Rearrange for $PMT$: $$PMT = \frac{FV \times i}{(1+i)^n - 1}$$ Substitute values: $$i = \frac{0.05}{12} \approx 0.0041667$$ $$(1+i)^n = \left(1+\frac{0.05}{12}\right)^{480} \approx 7.358416$$ $$PMT = \frac{2200000 \times 0.0041667}{7.358416 - 1} \approx \frac{9166.74}{6.358416} \approx 1442$$

Answer:

The monthly deposit is $\boldsymbol{1442}$