Help please compiFind the compound amount and the amount of interest earned by the following deposit.$5100 at 3.6% compounded continuously for 8 years.The future value after 8 years is approximately $(Do not round until the final answer. Then round to the nearest cent as needed.)Enter your answer in the answer box.earch

Answered: Find the compound amount and the amount…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter7: Exponents And Exponential Functions

Section7.8: Transforming Exponential Expressions

Problem 3PPS

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Find the compound amount and the amount of interest earned by the following deposit.
$5100 at 3.6% compounded continuously for 8 years.
The future value after 8 years is approximately $
(Do not round until the final answer. Then round to the nearest cent as needed.)
Enter your answer in the answer box.
earch

Expert Solution

Step 1

Given that principal, P = $5100, at rate, R = 3.6% for time, n = 8 years

the amount after 8 years will be A, then

$A = P {(1 + \frac{R}{100})}^{n}$

now,

$\begin{array}{rcl} A & = & $ 5100 \times {(1 + \frac{3.6}{100})}^{8} \\ = & $ 5100 \times {(1 + \frac{36}{1000})}^{8} \\ = & $ 5100 \times {(1 + 0.036)}^{8} \\ = & $ 5100 {\times (1.036)}^{8} \\ = & $ 5100 \times 1.3270217568054 \\ = & $ 6767.8109597080 \\ A & = & $ 6767.81 \end{array}$

$\begin{array}{rcl} I n t e r e s t, I & = & A - P \\ = & $ 6767.81 - $ 5100 \\ = & $ 1667.81 \end{array}$

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