If I invest 5,000 at a rate 8.5% for 13 days? How much interest will I earn on my investment if the interest is compounded daily?
I need help with setting up formula or help in general. Any help is appreciated.
since the 8.5% is annual interest, divide it by 365 for the daily rate. Then the interest will be the final balance less the original amount:
5000((1+.085/365)^13 - 1) = $15.16
P = Po(1+r)^n.
r = 0.085/365 = 0.000233 = daily % rate.
n = 13 Compounding periods.
P = 5000(1+0.000233)^13 = $5015.17
Int. = P - Po = 5015.17 - 5000 = $15.17.
To calculate the interest earned on an investment with daily compounding, you can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the time period (in years)
Let's break down the problem:
Principal amount (P) = $5,000
Annual interest rate (r) = 8.5% = 0.085
Time period (t) = 13 days = 13/365 years (since interest rate is given on an annual basis)
Number of times compounded per year (n) = 365 (since interest is compounded daily)
Now, substitute these values into the formula:
A = 5000(1 + 0.085/365)^(365*(13/365))
Simplifying this,
A = 5000(1 + 0.000232)^365
A = 5000(1.000232)^365
A ≈ 5000(1.08767)
A ≈ $5,438.35
To find the interest earned (I), subtract the principal amount from the future value:
I = A - P
I = $5,438.35 - $5,000
I ≈ $438.35
Therefore, if you invest $5,000 at a rate of 8.5% with daily compounding for 13 days, you will earn approximately $438.35 in interest on your investment.