Question

Naomi invested $920 in a account paying an interest rate of 4.7% 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 $2310

Answer 1

19 years

Explanation:

Answer 2

We can use the continuous compound interest formula:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate (as a decimal), and t is the time (in years). We can rearrange this formula to solve for t:

t = ln(A/P) / r

where ln is the natural logarithm function.

Using the given values, we have:

P = 920

A = 2310

r = 0.047

So,

t = ln(2310/920) / 0.047

t ≈ 18.8 years

Rounding to the nearest year, it would take about 19 years for the value of the account to reach $2310.