Question

Elena is thinking about putting $200 in a savings account that earns 4% interest compounded semiannually. She wants to keep that money in the account for 4 years. Which of the formulas below can help her calculate how much money she will have at the end of the 4 years?

Answer 1

Answer: The required formula is,

`200(1+0.02)^8`

Explanation:

Here, the principal amount, P = $ 200,

Annual rate of interest, r = 4 %,

Time, t = 4 years,

Number of periods in one year( semiannual in one year ), n = 2

Thus, the amount after 4 years, compounded semiannually is,

`A=P(1+(r/n)/(100))^(nt)`

`=200(1+(4/2)/(100))^(2* 4)`

`=200(1+(2)/(100))^8`

`=200(1+0.02)^8`

Which is the required formula.