Question

Suppose, That your friend was born , your friends parents deposited $4000 in an account paying 5.5% interest compounded quarterly.What will the account balance be after 14 years ?

Answer 1

To calculate the future value of a $4000 deposit at 5.5% interest compounded quarterly after 14 years, use the compound interest formula A = P(1 + r/n)^(nt) with P=$4000, r=0.055, n=4, and t=14.

Step-by-step explanation:

The question asks for the future value of a $4000 deposit in an account with a 5.5% interest rate compounded quarterly after 14 years. To solve this, one would use the compound interest formula, which is 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.

In this example:

• P = $4000
• r = 5.5% or 0.055
• n = 4 (because the interest is compounded quarterly)
• t = 14 years

Plugging the values into the compound interest formula gives:

A = $4000(1 + 0.055/4)^(4*14)

Calculating this will give the final balance of the account after 14 years.

Answer 2

`\bf \qquad \textit{Compound Interest Earned Amount}\\\\ A=P\left(1+(r)/(n)\right)^(nt) \qquad \begin{cases} A=\textit{current amount}\\ P=\textit{original amount deposited}\to &\$4,000\\ r=rate\to 5.5\%\to (5.5)/(100)\to &0.055\\\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{compounds quarterly, every}\\ \textit{quarter, thus 4 times} \end{array}\to &4\\\\ t=years\to &14 \end{cases}`