suppose your friend's parents invest $20,000 in an account paying 6% annually. what will the balance be after 6 years?
If accumulated but not compounded
.06 * 20,000 = 1200 per year
1200 * 6 = 7200 total interest
7200 + 20,000 = 27,200
If compounded annually
20,000 * 1.06^6 = 20,000*1.4185 = 28,370.38
thank you so much
To calculate the balance after 6 years, we'll use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/ balance after time t
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
In this case, the principal amount (P) is $20,000, the annual interest rate (r) is 6% which can be expressed as 0.06 in decimal form, and the investment is compounded annually (n = 1). We need to find the future value after 6 years (t = 6).
Plugging in the values into the formula:
A = 20,000(1 + 0.06/1)^(1*6)
Simplifying:
A = 20,000(1.06)^6
Using a calculator, raise 1.06 to the power of 6:
A ≈ 20,000(1.4185)
A ≈ $28,370
Therefore, the balance after 6 years would be approximately $28,370.
To calculate the balance after 6 years with an annual interest rate of 6%, we can use the formula for compound interest:
Balance = Principal * (1 + Interest Rate)^Time
Here, the principal (P) is $20,000, the interest rate (R) is 6% (or 0.06 in decimal form), and the time period (T) is 6 years. Let's substitute these values into the formula:
Balance = $20,000 * (1 + 0.06)^6
Now, let's calculate the balance:
Balance = $20,000 * (1.06)^6
= $20,000 * 1.418519
= $28,370.38
After 6 years, the balance in your friend's parents' account will be approximately $28,370.38.