Answer: $1,073,731.76
Explanation:
This question refers to an annuity which is the payment of a series of cash.
It relates to the future value of an annuity because the question asks what the retirement income will be in 30 years.
The formula for the future value of an annuity is,
F = P * ([1 + r]^n - 1 )/r
Where,
P is the payment amount.
r is equal to the interest (discount) rate and
n is the number of periods.
As the details given to us are in a yearly format but the payments are monthly we would need to convert these details as well.
r = 0.10/12
= 0.10/12
It's best to leave it as a fraction
n = 30 * 12 months
= 360 months.
Now we plug them into the formula.
= 475 * ( (1+(0.1/12))^360 - 1)/(0.1/12)
= $1,073,731.76
This is the value in 30 years.
If you need any clarification or have any questions please feel free to comment or react. Thank you.
The amount in the retirement account be in 30 years is $1,073,731.76.
Since the monthly deposit is $475. Here the monthly interest rate is 10%.And the time period is 30 years
Now here we applied the formula of future value of annuity
So,
FVA = C{[(1 + r)^t− 1] / r}
= $475[{[1 + (0.10/12)]^360 – 1} / (0.10/12)]
= $1,073,731.76
hence, The amount in the retirement account be in 30 years is $1,073,731.76.
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