Question

Use the compound interest formulaA(t)=P(1+r/n))^ntand round to the nearest hundredths place, if necessary.An account is opened with an initial deposit of $6,500 and earns 3.6% interest compounded semi annually.What will the account be worth in 20 years?How much would the account have been worth if the interest were compounding weekly?

Answer 1

a) In 20 years, the account will be worth $13268.58

b) The account will be worth $13350.52

Explanation:

a) Principal = P = $6500

rate = r = 3.6% = 0.036

time = t = 20 years

n = number of times it was compounded

n = semi-annually = 2

Using the compound interest formula:

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

inserting the values in the equation above:

$\begin{gathered} A(t)\text{ = 6500(1 +}\frac{0.036}{2})^{2\times20} \\ A(t)\text{ = 6500(1 +}0.018)^{40}\text{ = 6500(1}.018)^{40} \\ A(t)\text{ = 13268.58} \end{gathered}$

In 20 years, the account will be worth $13268.58

b) n = compunded weekly

n = 52

Principal = P = $6500

rate = r = 3.6% = 0.036

time = t = 20 years

$\begin{gathered} A(t)\text{ = 6500(1 +}\frac{0.036}{52})^{52\times20} \\ A(t)\text{ = 6500(1 +}\frac{0.036}{52})^{52\times20} \\ A(t)\text{ = }13350.52 \end{gathered}$

The account will be worth $13350.52