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 \% = (9)/(100) = 0.09`

t = 3 years

Substituting the values we get,

`A = 9500e^(0.09 * 3)\\\\A = 9500 * e^(0.27)\\\\A = 9500 * 1.309964\\\\A = 12444.66`

Thus amount in account after 3 years is $ 12444.66