Question

Howard invested $5,000 in Certificate of Deposit (CD) that pays 3.75% interest. compounded weekly. What is the value of the CD at the end of the 4 years?

Answer 1

Answer:

The value of the CD at the end of the 4 years is $5,808.86.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Howard invested $5,000 in Certificate of Deposit (CD) that pays 3.75% interest.

This means that $P = 5000, r = 0.0375$

Compounded weekly

An year has 52 weeks, so $n = 52$

Then

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(t) = 5000(1 + \frac{0.0375}{52})^{52t}$

What is the value of the CD at the end of the 4 years?

This is A(4). So

$A(4) = 5000(1 + \frac{0.0375}{52})^{52*4} = 5808.86$

The value of the CD at the end of the 4 years is $5,808.86.