Question

you deposit $4000 in an account earning 4% interest compounded quarterly. How much will you have in the account 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 &\$4000\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ 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 = 4000\left(1+(0.04)/(4)\right)^(4\cdot 10)\implies A=4000(1.01)^(40) \implies A \approx 5955.45`

Answer 2

$5955.45

Explanation:

We can use the formula to find the sum of the money, when we calculate the amount of money according to compound interest.

Before we getting ready to solve the sum, we have to keep these points in our mind.

1. Interest will calculate quarterly. So, we have to divide the interest by 4.
2. I year has 4 quarters. So, number of years should me multiply by 4.

Formula to find the sum of money after compound interest is:

`\sf S = X ( 1 + r )^n`

Here,

S = Sum of money

X = Amount of money deposited

r = Interest rate

n = Time ( in years )

Let us solve it now.

`\sf S = X ( 1 + r )^n\\\\\sf S = 4000 ( 1 + (4)/(100)*(1)/(4) )^4^0\\\\\sf S = 4000 ( 1 + (4)/(400) )^4^0\\\\\sf S = 4000 ( 1 + 0.01 )^4^0\\\\\sf S = 4000 ( 1.01 )^4^0\\\\\sf S = 5955.45`