Respuesta :
We have been given that miss Roxanne is 25 years old and she puts 1800 dollars per quarter that returns 6% interest.
(a) We need to figure out how much will be in the account when she turns 65 years old. When she turns 65 years old, the number of years during which she made deposits would be 40. Since she made quarterly deposits. She made a total of 160 deposits. We can now figure out the final amount in the account using future value of annuity formula.
[tex]A=P\frac{(1+r)^{n}-1}{r}[/tex]
We have the values P=1800, r=6/4% = 1.5% = 0.015 and n=160.
Therefore, the amount in the account would be:
[tex]A=1800\frac{(1+0.015)^{160}-1}{0.015}=1179415.39[/tex]
Therefore, miss Roxanne will be 1179415.39 dollars in her account when she turns 65 years old.
(b) In this part we need to figure out the total amount she deposited.
The total amount she deposited would be [tex]1800*160=\$288000[/tex].
(c) We can find the interest earned by subtracting her contribution from the answer of part (a).
Interest earned = [tex]1179415.39-288000=\$891415.39[/tex]
a. The amount that will be in her account when she will turn 65 years is $1,179,415.39 .
b. The total contribution to the account by her is $288,000 .
c. The interest earned by her is $891,415.39 .
Further Explanation:
a.
In order to calculate the amount that will be in her account when she is 65 years old, we will find the future value. The Future Value is used to calculate the futuristic value of cash flow.
The formula to future value (FV) is:
[tex]\begin{gathered} {\text{FV of the annuity = P }}\left( {\frac{{{{(1 + r)}^n} - 1}}{r}} \right) \\ {\text{P = Periodic Payment}} \\ r = {\text{ rate per period}} \\ n = {\text{ number of periods}} \\ \end{gathered}[/tex]
Calculate the Future Value:
Rate per period:
[tex]\begin{gathered} r = \frac{{6\% }}{4} \\ = 1.5 \\ \end{gathered}[/tex]
Future value:
[tex]\begin{gathered} {\text{Future}}\,{\text{value}} = {\text{ \$ 1,800}}\left( {\frac{{{{(1 + 0.015)}^{160}} - 1}}{{0.015}}} \right) \\ = \$ 1,800 \times 655.23 \\ = \$ 1,179,415.39 \\ \end{gathered}[/tex]
The amount that will be in her account when she will turn 65 years is $1,179,415.39
b.
Calculate her total contribution to the account:
Total contribution = $1,800 × 4 × 40
= $288,000
Her total contribution to the account is $288,000.
c.
Calculate the interest she earned:
Interest = $1,179,415.39 - $288,000
= $891,415.39
The interest earned by her is $891,415.39.
Learn more:
1. Present value of allowance
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3. Net present value
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Answer details:
Grade: High School
Subject: Financial Management
Chapter: Time value of money
Keywords: Miss Roxanne Davenport is 25 years old, puts away $1,800 per quarter in an account returns 6% interest, Account when she turns 65, her total contribution to the account, interest she earn, time value of money, future value, present value, NPV, PV.
