MATH SOLVE

5 months ago

Q:
# 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

Accepted Solution

A:

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,[tex] A = P(1+r)^t[/tex]Where, A = last amount, P = principal amount, r = rate of interest, t = number of years.Here, P = $20,000, r = 5% = [tex] \frac{5}{100} = 0.05 [/tex], t = [tex] (50-25) = 25[/tex] years.By substituting the values in the formula we will get,[tex] A = 20000(1+0.05)^{25}[/tex][tex] A = 20000(1.05)^{25}[/tex][tex] A = 20000(3.38635494)[/tex][tex] A = 67727.10[/tex] ( 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 = [tex] (50-35) = 15[/tex] years.[tex] A = 20000(1+0.05)^{15}[/tex][tex] A = 20000(1.05)^{15}[/tex][tex] A = 20000(2.078928)[/tex][tex] A = 41578.56[/tex]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 = $ [tex] (67727.10 - 41578.56) [/tex] = $ 26148.54 = $26149.So we have got the required answer.Option D is correct here.