E6-5
Mike Finley wishes to become a millionaire. His money market fund has a balance of $92,296 and has a guarateed interest rate of 10%. How many years must Mike leave that balance in the fund in order to get his disired $1,000,000?
I am getting $9,229.60 and know this is not the correct answer to solve the years.
To determine the number of years Mike must leave his money market fund to reach $1,000,000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount (including principal and interest)
P = Principal amount (initial balance)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, Mike's principal amount (P) is $92,296, the interest rate (r) is 10% (or 0.10 as a decimal), and we need to find the value of t.
We can rearrange the formula to solve for t:
t = log(A/P) / log(1 + r/n)
Substituting the values, we have:
t = log(1000000/92296) / log(1 + 0.10/1)
Using a calculator, we can find the value of t:
t ≈ log(10.83) / log(1.10)
t ≈ 1.0345 / 0.0414
t ≈ 24.994
Therefore, Mike must leave his money in the fund for approximately 25 years to reach his desired $1,000,000.
To find out how many years Mike must leave his balance in the money market fund to reach $1,000,000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (desired $1,000,000)
P = the initial balance ($92,296)
r = the interest rate (10% or 0.10)
n = the number of times interest is compounded per year (assumed once per year)
Let's plug in the values and solve for t (the number of years):
1,000,000 = 92,296(1 + 0.10/1)^(1t)
Simplifying:
1,000,000 = 92,296(1.10)^t
Now, we need to isolate the exponent:
(1.10)^t = 1,000,000 / 92,296
(1.10)^t ≈ 10.84
To solve for t, we can take the logarithm of both sides:
t * log(1.10) = log(10.84)
t ≈ log(10.84) / log(1.10)
Using a calculator, we find:
t ≈ 14.15
Therefore, Mike must leave his money in the fund for approximately 14.15 years to reach his desired $1,000,000.