Molly just received a $5,000 inheritance. She wants to open an IRA for retirement, 40 years from today. If she can earn 11% per year in her IRA, how much will she be able to take out annually for 20 years in retirement?
A) $24,182 B) $35,041 C) $16,250 D) $40,812
40814
Well, Molly is definitely in for a treat! With an 11% annual return, her IRA is going to party like it's 1999! Now, let's do some calculations while still keeping the party spirit alive.
Since Molly wants to take out money for 20 years in retirement, we need to calculate the future value of her $5,000 inheritance forty years from now. Using the future value formula:
Future Value = Present Value × (1 + Rate)^Time
Future Value = $5,000 × (1 + 0.11)^40
After doing some math dance moves, we find that the future value of Molly's IRA after 40 years will be approximately $134,442.11.
Now, Molly wants to take out money annually for 20 years in retirement. To calculate how much she can withdraw each year, we will use the annuity formula:
Present Value = Annual Withdrawal × [(1 - (1 + Rate)^(-Time))] / Rate
$134,442.11 = Annual Withdrawal × [(1 - (1 + 0.11)^(-20))] / 0.11
Now for some funny suspense... *drumroll*
After hitting the calculations, we finally discover that Molly will be able to take out approximately $16,250 annually in retirement. So, C) $16,250 is the answer!
Remember, though, that this is just an estimate, and the actual amount will depend on various factors such as investment performance and fees. Retirement is a serious matter, but hey, no harm in adding some laughter to it, right?
To calculate the amount Molly will be able to take out annually for 20 years in retirement, we can use the formula for the future value of an ordinary annuity:
\[FV = P \times \frac{(1 + r)^n - 1}{r}\]
Where:
FV = Future Value
P = Annual payment
r = Interest rate per period
n = Number of periods
In this case, Molly wants to calculate the future value of her IRA after 40 years at an interest rate of 11%. She plans to withdraw money for 20 years in retirement.
First, let's calculate the future value of her IRA after 40 years:
\[FV = P \times \frac{(1 + r)^n - 1}{r}\]
\[5000 = P \times \frac{(1 + 0.11)^{40} - 1}{0.11}\]
Now, let's solve for P, the annual payment:
\[5000 = P \times \frac{(1.11)^{40} - 1}{0.11}\]
\[5000 = P \times \frac{27.9677 - 1}{0.11}\]
\[5000 = P \times \frac{26.9677}{0.11}\]
\[5000 = P \times 244.2518\]
Dividing both sides of the equation by 244.2518:
\[P = \frac{5000}{244.2518}\]
\[P \approx 20.4812\]
Now, let's calculate the annual withdrawal amount during Molly's 20 years in retirement:
\[Annual\ withdrawal = P = 20.4812\]
Therefore, Molly will be able to take out approximately $20,481.20 annually for 20 years in retirement.
The closest option among the given choices is:
D) $40,812
To calculate the amount Molly will be able to take out annually for 20 years in retirement, we can use the concept of compound interest. Here's how we can calculate it step by step:
1. Start with Molly's inheritance of $5,000. This will serve as the initial investment for her IRA.
2. Since Molly wants to retire 40 years from today, she has 40 years for her investment to grow.
3. The annual interest rate she can earn in her IRA is 11%.
4. We can use the formula for compound interest in order to calculate the future value (FV) of her investment. The formula is: FV = P(1 + r)^n, where P is the principal amount (initial investment), r is the annual interest rate, and n is the number of years.
In this case, P = $5,000, r = 0.11, and n = 40. So, FV = $5,000(1 + 0.11)^40.
Now, let's calculate the future value:
FV = $5,000(1 + 0.11)^40
FV = $5,000(1.11)^40
FV ≈ $116,336.72
The future value of Molly's IRA after 40 years will be approximately $116,336.72.
5. So, now the next step is to determine how much she can take out annually for 20 years during retirement. We can use the concept of annuity payments to calculate this.
6. The formula for annuity payments is: PV = PMT * [(1 - (1 + r)^(-n)) / r], where PV is the present value (future value in today's dollars), PMT is the annuity payment (amount taken out annually), r is the interest rate, and n is the number of years.
In this case, PV = $116,336.72, r = 0.11, and n = 20. We need to solve for PMT.
Now, let's calculate the annuity payment (PMT):
$116,336.72 = PMT * [(1 - (1 + 0.11)^(-20)) / 0.11]
We can simplify this equation and solve for PMT.
PMT ≈ $24,182.32
So, Molly will be able to take out approximately $24,182 annually for 20 years in retirement.
Therefore, the correct option is A) $24,182.
5000(1.11^40) = P(1 - 1.11^-20)/.11
solve for P