If you invest $50,000 to earn 8% interest, which of the following compounding approaches would return the lowest amount after one year?
a. daily
b. monthly
c. quarterly
d. Annually
To determine which compounding approach would return the lowest amount after one year, we need to compare the total amount earned after one year using each compounding approach. The formula to calculate the total amount is:
A = P(1 + r/n)^(n*t)
Where:
A = the total amount after t years
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Let's calculate the total amount for each compounding approach and compare the results.
a. Daily compounding:
In this case, interest is compounded 365 times a year (since there are 365 days in a year). So, n = 365.
A = 50000(1 + 0.08/365)^(365*1)
Calculating this equation would give you the total amount after one year.
b. Monthly compounding:
Here, interest is compounded 12 times a year (since there are 12 months in a year). So, n = 12.
A = 50000(1 + 0.08/12)^(12*1)
Calculate this equation to find the amount after one year.
c. Quarterly compounding:
Interest is compounded 4 times a year (since there are 4 quarters in a year). So, n = 4.
A = 50000(1 + 0.08/4)^(4*1)
Calculate this equation to get the total amount after one year.
d. Annually compounding:
In this case, interest is only compounded once a year. So, n = 1.
A = 50000(1 + 0.08/1)^(1*1)
Calculate this equation to find the amount after one year.
After calculating the total amount for each approach, compare the results to determine which one returns the lowest amount.