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:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
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 [tex]P = 5000, r = 0.0375[/tex]
Compounded weekly
An year has 52 weeks, so [tex]n = 52[/tex]
Then
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 5000(1 + \frac{0.0375}{52})^{52t}[/tex]
What is the value of the CD at the end of the 4 years?
This is A(4). So
[tex]A(4) = 5000(1 + \frac{0.0375}{52})^{52*4} = 5808.86[/tex]
The value of the CD at the end of the 4 years is $5,808.86.
