You are currently investing your money in a bank account which has a nominal annual rate of 8 percent, compounded annually. If you invest $2,000 today, how many years will it take for your account to grow to $10,000?
20000
To solve this problem, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (in this case, $10,000)
P = the principal amount (in this case, $2,000)
r = the nominal annual interest rate (in this case, 8% or 0.08)
n = the number of times interest is compounded per year (in this case, once annually)
t = the number of years
We want to solve for t, so we will rearrange the formula as follows:
t = (log(A/P) / (n * log(1 + r/n)))
Using the given values, we can substitute them into the formula and solve for t:
t = (log(10,000/2,000) / (1 * log(1 + 0.08/1)))
Calculating the logarithms, we get:
t = (log(5) / (1 * log(1.08)))
By evaluating the logarithms, we find:
t ≈ 14.21
Therefore, it will take approximately 14.21 years for the account to grow to $10,000.