Q 12.59 New grandparents decide to inves... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q 12.59 (page 1196)

New grandparents decide to invest $$ 200$ per month in an annuity for their grandson. The account will pay $5 %$ interest per year which is compounded monthly. How much will be in the child鈥檚 account at his twenty-first birthday?

Short Answer

Expert verified

Amount in child's account will be equal to $$ 88868.36$

Step by step solution

Step 1. Given information

Amount of $$ 200$ is invested per month in an annuity such that their account will pay 5% interest per year which is compounded monthly.

Step 2. Find the amount in child’s account at his twenty-first birthday.

Let $P, r, n, t$ denote amount invested, rate of interest, the number of times the deposit will be made and the interest compounded each year and number of years.

$\begin{array}{rcl} P & = & $ 200 \\ r & = & 0.05 \\ n & = & 12 \\ t & = & 21 \end{array}$

So,

To find the Annuity formula, use the formula $\begin{array}{rcl} A_{t} & = & \frac{P ({(1 + \frac{r}{n})}^{n t} - 1)}{\frac{r}{n}} \end{array}$ localid="1645377646619" $\begin{array}{rcl} A_{t} & = & \frac{200 ({(1 + \frac{0.05}{12})}^{12 (21)} - 1)}{\frac{0.05}{12}} \\ = & 48000 ({(1 + \frac{0.05}{12})}^{252} - 1) \\ = & $ 88868.36 \end{array}$

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91影视

New grandparents decide to invest $$ 200$ per month in an annuity for their grandson. The account will pay $5 %$ interest per year which is compounded monthly. How much will be in the child鈥檚 account at his twenty-first birthday?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the amount in child’s account at his twenty-first birthday.

One App. One Place for Learning.

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91影视

New grandparents decide to invest $200per month in an annuity for their grandson. The account will pay 5%interest per year which is compounded monthly. How much will be in the child鈥檚 account at his twenty-first birthday?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the amount in child’s account at his twenty-first birthday.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Calculus

Mechanics Maths

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

New grandparents decide to invest $$ 200$ per month in an annuity for their grandson. The account will pay $5 %$ interest per year which is compounded monthly. How much will be in the child鈥檚 account at his twenty-first birthday?