Question

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

Answer 1

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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.