Answer: A) The amount needed at the beginning would be $146,342
B) The total money you would pull out would be $300,001
C) The interest earned would total $153,659
Explanation: If you planned on withdrawing 20000 per year for 15 years, that would be a total of 300000 at the end of 15 years. The interest you would have earned is calculated as;
I = PRT
Note that the addition of your interest and the sum invested (Principal) shall be a total of 300000. Hence,
I + P = 300000
Making P the subject of the equation,
P = 300000 - I.
So we have, R as 0.07, T as 15 and P as 300000 - I, we can now substitute for the values as follows;
I = PRT
I = (300000 - I) x 0.07 x 15
I = (300000 - I) x 1.05
I = 315000 - 1.05I
Collecting like terms we now have
I + 1.05I = 315000
2.05I = 315000
Divide both sides of the equation by 2.05
I = 153659 (approximately)
If the interest earned is $153,659, and the amount you wish to withdraw at the end of 15 years is a total of $300,000, then the principal (P) invested would be
I = PRT
I/RT = P
153659/(0.07 x 15) = P
146341.9 = P
P≈ 146342
Therefore, interest earned = $153,659
Principal invested = $146,342
Total withdrawal = $300,001
Answer:
a) How much do you need in your account at the beginning?
b) How much total money will you pull out of the account?
c) How much of that money is interest?
Explanation:
We need to calculate the present value of the annuity:
PV of annuity = P x {[1 - (1 + r)⁻ⁿ] / r}
PV of annuity = $20,000 x {[1 - (1 + 7%)⁻¹⁵] / 7%}
= $20,000 x {[1 - 1.07⁻¹⁵] / 7%} = $20,000 x (0.63755398 / 7%) = $20,000 x 9.107914 = $182,158.28
total money pulled out = $20,000 x 15 payments = $300,000
total interest received = $300,000 - $182,158.28 = $117,841.72
