Question

If you invest $25000 in an account that gets 12% annual interest compounded quarterly, how much would you have in 10 years?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$25000\\ r=rate\to 12\%\to (12)/(100)\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 25000\left(1+(0.12)/(4)\right)^(4\cdot 10)\implies A=25000(1.03)^(40) \implies A \approx 81550.94`

Answer 2

After 10 years, the $25,000 investment at an annual interest rate of 12% compounded quarterly will amount to approximately $98,347.05. To calculate how much you would have in your account after 10 years when investing $25,000 with an annual interest rate of 12% compounded quarterly, you can use the formula for compound interest: A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

For this question:

• P = $25,000
• r = 12% or 0.12
• n = 4 (because the interest is compounded quarterly)
• t = 10 years

Plugging these values into the formula, we get:

A = 25000(1 + 0.12/4)^(4*10) = 25000(1 + 0.03)^(40) = 25000(1.03)^40

Calculating this expression, we find that the investment will grow to:

A = $98,347.05 (rounded to two decimal places).

Therefore, after 10 years, with the power of compound interest, the $25,000 investment at an annual interest rate of 12% compounded quarterly will amount to approximately $98,347.05.