Question

Find the amount of money that will be accumulated in a savings account if $4175 is invested at 6.0% for 17 years and the interest is compounded continuously. Round your answer to two decimal places.

Answer 1

Answer:

11,242.37

Step-by-step explanation:

principal=$4175

rate=6%

time=17 years

$amount = \: pricipal (1 + \frac{rate}{100} )^{time \\ }$

$= 4175(1 + \frac{6}{100} )^{17} \\ \\ = 4175 \times ( \frac{106}{100}) ^{17 \\ } \\ \\ = 4175 \times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100}\times \frac{106} {100} \\ \\ = 4175 \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \times \frac{53}{50} \\ \\ or \\ \\ = 4175 \times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06\times 1.06 \\ \\ = 11242.37(approx)$