suppose that when your friend was born your friends parents deposited $4000 in an account paying 4.1% interest compounded quarterly. what will the account balance be after 15 years?
To calculate the account balance after 15 years, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future account balance
P = the initial deposit or principal amount ($4000 in this case)
r = the annual interest rate (4.1% expressed as decimal, so 0.041)
n = the number of compounding periods per year (quarterly compounding, so 4)
t = the number of years (15 in this case)
Now we can substitute the values into the formula and calculate the account balance:
A = 4000(1 + 0.041/4)^(4*15)
Step 1: Calculate the value inside the brackets:
(1 + 0.041/4) = 1.01025
Step 2: Raise this value to the power of (4*15):
(1.01025)^(4*15) = 1.01025^60 ≈ 1.81147
Step 3: Multiply this value by the initial deposit:
4000 * 1.81147 ≈ $7,245.88
Therefore, the account balance after 15 years will be approximately $7,245.88.
To calculate the account balance after 15 years with quarterly compounding interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final account balance
P = the initial deposit
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $4000
r = 4.1% = 0.041 (as a decimal)
n = 4 (quarterly compounding)
t = 15
Substituting these values into the formula:
A = 4000(1 + 0.041/4)^(4*15)
A = 4000(1 + 0.01025)^(60)
Calculating the expression inside the parentheses:
A = 4000(1.01025)^(60)
Using a calculator or spreadsheet, we can find:
A ≈ $4000 * 1.744275578
A ≈ $6977.10
Therefore, the account balance after 15 years will be approximately $6,977.10.