If $13,000 is deposited in a bank account paying 6% compounded quarterly, what amount will be in the account after 8 years? How much interest will be earned during the 8 years?
The amount after 8 years will be $___
How much interest will be earned during the 8 years? _____
r = 6% / 4 = 1.5% = 0.015 = Rate /qtr.
n = 8 yrs * 4 comp. /yr = 32 comp.
Pt = Po(1 + r)^n,
=13000(1.015)^32,
= 13000 * 1.6103 = 20934.22.
I = Pt - Po = 20934.22 - 13000 = 7934.22.
To find the amount in the account after 8 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, we have:
P = $13,000
r = 6% = 0.06 (as a decimal)
n = 4 (compounded quarterly)
t = 8 years
Substituting the values into the formula:
A = $13,000(1 + 0.06/4)^(4*8)
A ≈ $13,000(1 + 0.015)^32
A ≈ $13,000(1.015)^32
A ≈ $13,000(1.53862)
A ≈ $19,999.06
Therefore, the amount in the account after 8 years will be approximately $19,999.06.
To calculate the interest earned during the 8 years, we can subtract the initial deposit from the final amount:
Interest = Final amount - Initial deposit
Interest = $19,999.06 - $13,000
Interest ≈ $6,999.06
Therefore, the interest earned during the 8 years will be approximately $6,999.06.
To find the amount in the account after 8 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount (P) is $13,000, the annual interest rate (r) is 6% (or 0.06 as a decimal), the interest is compounded quarterly, so the number of times interest is compounded per year (n) is 4, and the number of years (t) is 8.
Substituting these values into the compound interest formula:
A = 13,000(1 + 0.06/4)^(4 * 8)
Now we can solve this equation to find the final amount in the account after 8 years.
Using a calculator or a math software, we get:
A ≈ $19,098.18
So, the amount in the account after 8 years will be approximately $19,098.18.
To find the interest earned during the 8 years, we can subtract the initial deposit (principal amount) from the final amount:
Interest = A - P
Interest ≈ $19,098.18 - $13,000
Interest ≈ $6,098.18
Therefore, the interest earned during the 8 years will be approximately $6,098.18.