Carlos invested $6,000 in a money market mutual fund that pays interest on a daily basis. The balance in his account at the end of 8 mo (245 days) was $6,230.23. Find the effective rate at which Carlos's account earned interest over this period (assume a 365-day year). (Round your answer to two decimal places.)
i - decimal interest rate per day
6230.23 = 6000(1+i)^245
1.0383717 = (1+i)^245
log 1.0383717 = 245 log (1+i)
log (1+i) = .0163528/245
1+i = 1.0001537
(1+i)^365 = 1.0577
so you make 5.78% per year
i put 5.78% and it says it's wrong.
To find the effective rate at which Carlos's account earned interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = The balance at the end of the investment period
P = The initial investment amount
r = The interest rate
n = The number of times interest is compounded per year
t = The time in years
Since Carlos's account earns interest on a daily basis, we need to adjust the formula accordingly. First, let's calculate the time in years:
Time in years = Number of days / Days in a year
Time in years = 245 days / 365 days
Next, let's plug in the given values:
A = $6,230.23
P = $6,000
t = 245 days / 365 days
Now we need to solve for the interest rate 'r'. Rearranging the formula, we have:
r = ((A/P)^(1/(n*t))) - 1
Since Carlos's money market mutual fund pays interest on a daily basis, interest is compounded daily (n = 365).
Now we can plug in the values and calculate the effective interest rate:
r = (($6,230.23/$6,000)^(1/(365*(245/365)))) - 1
Calculating this expression will give us the effective interest rate. Rounding the answer to two decimal places will give us the final result.