Question

If you were to place $5,000 in a savings account that pays 6% interest compounded continuously, how much money will you have after 4 years? Assume you make no other deposits or withdrawals.

A. $6,356.25
B. $11,821.07
C. $5,024
D. $6,312.38
...?

Answer 1

A. $6,356.25

Explanation:

To calculate the amount of money you will have after 4 years in a savings account with continuous compounding, we can use the formula:

A = P * e^(rt)

Where:

A = the amount of money accumulated after t years

P = the initial principal amount (in this case, $5,000)

e = the base of the natural logarithm (approximately 2.71828)

r = the annual interest rate (in decimal form, so 6% becomes 0.06)

t = the number of years (in this case, 4)

Plugging in the values, we get:

A = 5000 * e^(0.06 * 4)

Using a calculator, we can evaluate this expression:

A ≈ 5000 * 2.71828^(0.24)

A ≈ 5000 * 1.276281

A ≈ 6381.405

Rounding to the nearest cent, the amount of money you will have after 4 years is approximately $6,381.41.

Therefore, the closest answer option is A. $6,356.25.

Answer 2

Option D - $6312.38

Explanation:

Given : If you were to place $5,000 in a savings account that pays 6% interest compounded continuously.

To find : How much money will you have after 4 years?

Solution :

Using compound interest formula,

`A=P(1+r)^t`

Where A is the amount,

P is the principle P=$5000

r is the rate r=6%=0.06

t is the time t= 4 years

Substitute the value,

`A=P(1+r)^t`

`A=(5000)(1+0.06)^4`

`A=(5000)(1.06)^4`

`A=5000* 1.262`

`A=6312.38`

The money he have after 4 years is $6312.38

Therefore, Option D is correct.