You deposit $3000 in an account earning 3% interest compounded continuously. How much will you have in this account in 10 years?

1 Answer
Jul 11, 2018

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You will have approximately color(red)($4,049.58) in your account in 10 years.

Explanation:

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Since the interest is compounded continuously, we need to use the following formula to calculate the Future Value:

color(blue)(A = Pe^((rt), where

color(blue)(P) is the Principal Amount (Initial deposit)

color(blue)(r) is the Rate of Interest

color(blue)(t) is the Period of deposit

color(blue)(A) is the Future Value

Let us substitute the values from our problem to calculate the amount payable (Future Value) at the end of 10 years.

color(blue)(P=$3000

color(blue)(r = 0.03

color(blue)(t=10

Hence,

Future Value (A) = color(blue)(3000*e^((0.03)(10)

color(blue)(A = 3000 * e ^((0.30)

rArr $4049.576423

Hence,

color(blue)(A ~~ $4049.58)

Hence, we conclude that you will have approximately color(red)($4,049.58) in your account in 10 years.

Hope it helps.