How much would $200 invested at 5% interest compounded monthly be worth after 9 years? Round your answer to the nearest cent.
Answer:
The amount becomes 31450 cents.
Step-by-step explanation:
Formula for compounded monthly
\(Amount = P(1 + \frac{r}{12} )^{12t}\)
Where P is the principle, r is the rate ofinterest in the decimal form and t is the time in years.
As given
$200 invested at 5% interest compounded monthly for 9 years.
P = $200
5% is written in the decimal form
\(= \frac{5}{100}\)
= 0.05
r = 0.05
t = 9 years
Put in the formula
\(Amount = 200(1 + \frac{0.05}{12} )^{12\times 9}\)
\(Amount = 200(1 + 0.0042)^{12\times 9}\)
\(Amount = 200(1.0042)^{108}\)
\(Amount = 200\times 1.5725\ (Approx)\)
Amount = $ 314.5 (Approx)
As 1 dollar = 100 cents
Now convert $ 314.5 into cent.
$ 314.5 = 314.5 × 100
= 31450 cents
Therefore the amount becomes 31450 cents.