Shota invests $2000 in a certificate of deposit that earns 2% in interest each year. Write a function that gives the total value V(t), in dollars, of the investment t years from now. Do not enter commas in your answer. V(t)=

Identify Interest Type: Identify the type of interest being calculated. Since the problem states that the investment earns 2% in interest each year, this suggests that the interest is compounded annually.Write Compound Interest Formula: Write the formula for compound interest. The formula for compound interest is V(t) = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.Plug in Values: Plug in the values into the formula. Since the interest is compounded annually, n = 1. The principal P is $2000, the annual interest rate r is 2% or 0.02, and t is the number of years. So the formula becomes V(t) = 2000(1 + 0.02/1)^(1*t).Simplify the Formula: Simplify the formula. V(t) = 2000(1 + 0.02)^t V(t) = 2000(1.02)^t This is the function that gives the total value of the investment t years from now.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Shota invests
$2000 in a certificate of deposit that earns
2% in interest each year.
Write a function that gives the total value
V(t), in dollars, of the investment
t years from now. Do not enter commas in your answer.

V(t)=

Shota invests $\$ 2000$ in a certificate of deposit that earns $2 \%$ in interest each year. $\newline$ Write a function that gives the total value $V(t)$ , in dollars, of the investment $t$ years from now. $\newline$ Do not enter commas in your answer. $\newline$ $V(t)=$ $\square$

View step-by-step help

Home

Math Problems

Algebra 2

Write exponential functions: word problems

Full solution

Q. Shota invests

\$ 2000

in a certificate of deposit that earns

2 \%

in interest each year.

\newline

Write a function that gives the total value

V(t)

, in dollars, of the investment

t

years from now.

\newline

Do not enter commas in your answer.

\newline

V(t)=

\square

Identify Interest Type: Identify the type of interest being calculated. $\newline$ Since the problem states that the investment earns $2\%$ in interest each year, this suggests that the interest is compounded annually.
Write Compound Interest Formula: Write the formula for compound interest. $\newline$ The formula for compound interest is $V(t) = P(1 + \frac{r}{n})^{nt}$ , where $P$ is the principal amount, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the number of years.
Plug in Values: Plug in the values into the formula. $\newline$ Since the interest is compounded annually, $n = 1$ . The principal $P$ is $\$2000$ , the annual interest rate $r$ is $2\%$ or $0.02$ , and $t$ is the number of years. So the formula becomes $V(t) = 2000(1 + 0.02/1)^{(1\cdot t)}$ .
Simplify the Formula: Simplify the formula. $\newline$ $V(t) = 2000(1 + 0.02)^t$ $\newline$ $V(t) = 2000(1.02)^t$ $\newline$ This is the function that gives the total value of the investment $t$ years from now.