Question

Megan put $2400 in a savings account earning 2% interest compounded semi-annually 7 years ago. How much money is in her account now?

Answer 1

Money in Megan saving accounts is $2758.74

Explanation:

Formula for compound interest is given as,

`A=P\left(1+i\right)^(n)`

where, m : number of compounding periods per year

i : rate per compounding period = r/ m

n : total no. of compounding periods = m * no. of years.

P : principal ( present value)

A : amount ( future value ) at the end of n periods

Now calculate the value of above terms.

Since it is given that interest is compounded semi annually.

Therefore value of m is m = 2.

Given that rate is 2% that is, r = 0.02

Also number of years is 7 that is, t = 7

Therefore formula becomes,

`A=P\left(1+(r)/(m)\right)^(m * t)`

Substituting the values in the formula,

`A=2400\left(1+(0.02)/(2)\right)^(2 * 7)`

Simplifying,

`A=2400\left(1+0.01\right)^(14)`

`A=2400\left(1.01\right)^(14)`

`A=2400 * 1.149474213`

`A=2758.738111`

Rounding to two decimal places, A = $ 2758.74

Therefore, Megan has total of $ 2758.74 in her saving account.