Question

You want to go to europe 5 years from now, and you can save $3,800 per year, beginning one year from today. you plan to deposit the funds in a mutual fund that you think will return 8.5% per year. under these conditions, how much would you have just after you make the 5th deposit, 5 years from now?

Answer 1

Using the future value annuity to solve the question we proceed as follows:
FV of annuity=P{[(1+r)^n-1]/r}
P=periodic Payment
r=rate per period
n=number of periods
from the question:'
P=$3,800
r=8.5%
n=5 years
hence:
A=3800{[(1+0.085)^5-1]/0.085}
A=$22,516.42

Answer 2

The amount you will have after making 5th deposit is $\boxed{\ 22516.56}$.

Further Explanation:

Annuity is a series of payment that is made after equal interval of time.

Future value of annuity of payment $P$ for $n$ year if the return is $i$ can be expressed as,

$\boxed{{\text{Future}}\,{\text{value}} = P \times \dfrac{{{{\left( {1 + i} \right)}^n} - 1}}{i}}$

Given:

The rate of return $i$ is $8.5\%$.

Yearly payment $P$ is $\ 3800$ for $5$ years.

Calculation:

Substitute $3800$ for $P$, $5$ for $n$ and $0.085$ for $i$ to obtain the amount after $5\text{th}$ deposit.

$\begin{aligned}  {\text{Future}}\,{\text{value}}&= 3800\times \frac{{{{\left( {1 + 0.085} \right)}^5} - 1}}{{0.085}} \\&= 3800 \times \frac{{{{1.085}^5} - 1}}{{0.085}} \\ &= 3800 \times \frac{{1.50366 - 1}}{{0.085}} \\ &= 3800 \times \frac{{0.50366}}{{0.085}} \\ &= 22516.56 \\ \end{aligned}$

Hence, the amount you will have after making $5\text{th}$ deposit is $\boxed{\ 22516.56}$.

Learn more:

1. Learn more about inverse of the function https://brainly.com/question/1632445

2. Learn more about range and domain of the function https://brainly.com/question/3412497

3. Learn more about profit and loss https://brainly.com/question/2479097

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Investment and return

Keywords: Europe, $5$ years from now, deposit, save, mutual fund, beginning one year from today, under these condition, return, interest rate, $8.5\%$ interest rate per year, $5\text{th}$ deposit, future value, annuity.