Question

Danielle deposits $200 into a bank account that compounds interest at a monthly rate of 1%. If Danielle leaves her money in the bank for 5 years, how much will she have? *

Answer 1

Given that Danielle deposits $200 into a bank account that compounds interest at a monthly rate of 1%;

`\begin{gathered} \text{ Principal P = \$200} \\ \text{rate r = 1\% }=0.01 \\ \text{ number of times compounded per year }=12 \end{gathered}`

If Danielle leaves her money in the bank for 5 years;

`\text{time t }=5\text{ years}`

Recall that the formula for compound interest is;

`F=P(1+(r)/(n))^(nt)`

where F is the final value;

`\begin{gathered} F=P(1+(r)/(n))^(nt) \\ F=200(1+(0.01)/(12))^(12(5)) \\ F=200(1.000833333\ldots)^(60) \\ F=200(1.051249) \\ F=\text{ \$210.25} \end{gathered}`

Therefore, the amount she will have is;

`\text{ \$210.25}`