Question

Paisley is going to invest in an account paying an interest rate of 3.4% compounded semi-annually. How much would Paisley need to invest, to the nearest cent, for the value of the account to reach $400 in 16 years?

A. $233.23
B. $305.09
C. $333.83
D. $443.38

Answer 1

To find out how much Paisley needs to invest to reach $400 in 16 years, we use the compound interest formula and solve for the principal amount. The answer is approximately $333.83. The correct answer is option C.

Step-by-step explanation:

To calculate the amount Paisley would need to invest, we can use the compound interest formula. The formula is given by:

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

Where:
A is the final amount ($400)
P is the principal amount (the amount to be invested)
r is the annual interest rate (3.4%) represented as a decimal (0.034)
n is the number of times interest is compounded per year (2)
t is the number of years (16)

Substituting the given values into the formula, we get:

400 = P(1 + 0.034/2)^(2*16)

Using a calculator, we can solve for P and round to the nearest cent:

P ≅ $333.83