Question

Melanie invested $5,500 in an account paying an interest rate of 6.9% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 11 years?

Answer 1

the other user didn't round to the nearest dollar..

answer is actually 11749.

Compounded Continuously:

A=Pe^{rt}

A=Pe

rt

P=5500\ {35px}r=0.069\ {35px}t=11

P=5500r=0.069t=11

Given values

A=5500e^{0.069(11)}

A=5500e

0.069(11)

Plug in

A=5500e^{0.759}

A=5500e

0.759

Multiply

A=11748.7645718

A=11748.7645718

Use calculator (with e button)

A≈11748.76

Round to nearest dollar

A=11749

Answer 2

`A=\$11,748.76`

Explanation:

we know that

The formula to calculate continuously compounded interest is equal to

`A=P(e)^(rt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

`t=11\ years\\ P=\$5,500\\ r=6.9\%=6.9/100=0.069`

substitute in the formula above

`A=5,500(e)^(0.069*11)`

`A=5,500(e)^(0.759)`

`A=\$11,748.76`