Question

If $9500 is invested at an interest rate of 9%, compounded continuously, determine the balance in the account after 3 years. Use the formula A = Pe^rt
A. $12,302.78
B. $12,444.66
C. $13,616.63
D. $70,196.03

Answer 1

Option B

The amount in account after 3 years is $ 12444.66

Solution:

Given that,

$9500 is invested at an interest rate of 9%, compounded continuously

The formula for total amount when interest is compounded continuously:

$A = p e^{rt}$

Where "p" is the principal

"r" is the rate of interest

"t" is the number of years

In this problem,

p = 9500

$r = 9 \% = \frac{9}{100} = 0.09$

t = 3 years

Substituting the values we get,

$A = 9500e^{0.09 \times 3}\\\\A = 9500 \times e^{0.27}\\\\A = 9500 \times 1.309964\\\\A = 12444.66$

Thus amount in account after 3 years is $ 12444.66