What is the balance if principal is $4,800, for 5 years at yearly rate of 6%, and the compounded interest is 4 times a year?
5 years = 20 periods
.06/4 = .015
1.015^20 = 1.36855007
times 4,800 = $6464.90
Thank you. For the same question what is the answer if the n=∞ [compounded continuously]?
To calculate the compound interest in this scenario, we can use the formula:
A = P*(1 + r/n)^(n*t)
Where:
A = the final amount (balance)
P = principal (initial amount)
r = annual interest rate (written as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $4,800
r = 6% = 0.06
n = 4 (compounded 4 times a year)
t = 5 years
Plugging these values into the formula, we get:
A = 4800 * (1 + 0.06/4)^(4*5)
Now we can solve this equation to find the balance after 5 years.
Step 1: Simplify the fraction: 0.06/4 = 0.015
Step 2: Calculate the exponent: 4*5 = 20
Step 3: Calculate the parenthesis: (1 + 0.015)^(20)
Step 4: Raise to the power of 20: (1.015)^(20)
Step 5: Calculate the final amount: 4800 * (1.015)^(20)
Using a calculator or a spreadsheet software, you can evaluate the expression (1.015)^(20) to get 1.3485636.
Finally, multiply this result by 4800 to get the balance:
Balance = 1.3485636 * 4800 = $6,471.56
Therefore, the balance after 5 years with a principal of $4,800, a yearly interest rate of 6%, and compounded quarterly will be approximately $6,471.56.