Question

Sophia invested $79,000 in an account paying an interest rate of 6. 8% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $152,800?

Answer 1

The time taken in years for the value of the account to reach $152800 is 10 years

The principal amount = $79000

The interest rate = 6.8%

The compounded continuously

The final value = $152800

The compounded continuously

P(t) = P(0) × $e^{rt}$

Where P(t) is the final amount

P(0) is the principal amount

r is the interest rate

t is the time period

152800 = 79000× $e^{0.68t}$

Move 79000 to the right hand side of the equation

$e^{0.68t}$ = 152800 / 79000

Divide the terms

$e^{0.68t}$ = 1.93

t = 10 years

Hence, the time taken in years for the value of the account to reach $152800 is 10 years

Learn more about compound continuously here

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