Question

If you invest $10,205.30 into an account earning an annual interest rate of 4.434%, how much will you have in your account after 6 years if the interest is compounded monthly? If the interest is compounded weekly? it the interest is compounded continuously?A) If interest is compounded monthly: ____B) If interest is compounded weekly:___C) If interest is compounded continuously:___(Note: All answers should include a dollar sign and be accurate to two decimal places)

Answer 1

The formula for caluculating the compound amount is

For this question,

p = $10,205.3

r = 4.434% = 0.004434

t = 6

A.

If interest is compounded monthly,

n = 12

$\begin{gathered} A\text{ = 10205.3(}1+\frac{0.004434}{12})^{12(6)} \\ A=10205.3(1+0.003695)^{72} \\ A=\text{ 10205.3(}1.003695)^{72} \\ A=10205.3(1.30414) \\ A\text{ =\ 13,309}.22 \end{gathered}$

B.

If interest is compounded weekly:

n = 52

$\begin{gathered} A\text{ = }10250(1+\frac{0.004434}{52})^{52\text{ x 6}} \\ A=10250.3(1.000085)^{312} \\ A=\text{ 10205.3}(1.3046) \\ A\text{ = \ 1}3,314.23 \end{gathered}$

C. If interest is compounded continuously:

n =365,

$\begin{gathered} A\text{ = 10,205.3(1 + }\frac{0.004434}{365})^{365\text{ x 6}} \\ A=10,205.3(1+0.000012147)^{2190} \\ A=10,205.3(1.000012147)^{2190} \\ A=10,205.3(1.304766) \\ A=\text{ \ }13,315.53 \end{gathered}$

Hence,

If interest is compounded monthly, the value is $13,309.22

If interest is compounded weekly, the va;ue is $13,314.23

And If interest is compounded continuously, the value is $13,315.53.