Which account should Rohan choose in order to earn the most interest after leaving the account open for 5 years
In order to determine which account will earn the most interest for Rohan, we need to consider the interest rate and compounding frequency of each account. Let's assume that there are two options for Rohan:
Option 1: Account with an annual interest rate of 6%, compounded annually.
Option 2: Account with an annual interest rate of 5.75%, compounded quarterly.
To compare the accounts, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the amount after interest is added
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = compounding frequency per year
t = number of years.
Let's assume Rohan deposits $10,000 into each account.
For Option 1:
A = 10000(1 + 0.06/1)^(1*5)
A = 10000(1 + 0.06)^5
A ≈ 10000(1.06)^5
A ≈ $13,382.24
For Option 2:
A = 10000(1 + 0.0575/4)^(4*5)
A = 10000(1 + 0.0575/4)^20
A ≈ 10000(1.014375)^20
A ≈ $13,378.22
After evaluating both accounts, we can see that Option 1 will earn Rohan slightly more interest over 5 years. Therefore, Rohan should choose Option 1 to earn the most interest.