Question

will mark brainest?


Jill and Bill are the same age. Jill inherits $20,000 when she is 25, and invests it in an account earning 5% annual interest rate, compounded annually. Bill receives a $20,000 bonus at age 35, and then invests it in an account which also earns a 5% annual interest rate, compounded annually. How much more money does Jill have than Bill at age 50?
A) $0
B) $10,000
C) $18,075
D) $26,149

Answer 1

Given, at the age of 25, Jill had $20,000 and he invested it in an account earning at a rate of 5% compounded annually.

We have to find how much Jill will earn at a age of 50.

We will use compound interest formula. The formula is,

$A = P(1+r)^t$

Where, A = last amount, P = principal amount, r = rate of interest, t = number of years.

Here, P = $20,000, r = 5% = $\frac{5}{100} = 0.05$, t = $(50-25) = 25$ years.

By substituting the values in the formula we will get,

$A = 20000(1+0.05)^{25}$

$A = 20000(1.05)^{25}$

$A = 20000(3.38635494)$

$A = 67727.10$ ( Approximately taken upto two decimal place)

So we have got Jill will get at the age of 50 is $ 67727.10.

Now given, Bill had $20000 at the age of 35. He also invested it in an account which earns at a rate of 5% compounded annually.

Similarly we have to find the amount he will get at the age of 50.

So, P = $20000, r = 0.05, t = $(50-35) = 15$ years.

$A = 20000(1+0.05)^{15}$

$A = 20000(1.05)^{15}$

$A = 20000(2.078928)$

$A = 41578.56$

So we have got at the age of 50 Bill will get $ 41578.56.

At the age of 50, Jill have more money than Bill. The amount of money that Jill have more = $ $(67727.10 - 41578.56)$ = $ 26148.54 = $26149.

So we have got the required answer.

Option D is correct here.

Answer 2

Answer:

Jill invests her money for 25 years, where Bill only invests for 15. Because of compounding, the money grows exponentially.

Jill: A = 20,000(1 + .05)25 ≈ $67,727

Bill: A = 20,000(1 + .05)15 ≈ 41,578

Jill - Bill = $67,727 - $41,578 = $26,149

so therefore the answer is D)$26,149