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?

A. $200(1 + 0.02)8
B. $200(1 + 0.04)4
C. $200(1 + 0.02)4
D. $200(1 + 0.08)2

Answer 1

A.
`\$200(1 + 0.02)^8`

Explanation:

Since, the amount that compounded semiannually is,

`A=P(1+(r)/(2))^(2t)`

Where, P is the principal amount,

r is the annual rate ( in decimals ),

And, t is time ( in years ),

Here, P = $ 200,

r = 4 % = 0.04 ( 1 % = 0.01 ),

t = 4 years,

Hence, the amount after 4 years would be,

`A=200(1+(0.04)/(2))^(2* 4)`

`=200(1+0.02)^8`

⇒ First option is correct.