Set up the formula to find the balance after 8 years for a total of $12,000 invested at an annual
1 answer:
Answer:
A = 12000(1.0002466)²⁹²⁰
Step-by-step explanation:
The formula for the amount after compound interest is:
"A" is the amount, or balance.
"P" is the principal, or starting amount/investment.
"i" is the interest rate for each compounding period.
"n" is the number of compounding periods.
The interest rate each compounding period, "i", is calculated with i=r/c
"r" is the annual interest rate in decimal form.
"c" is the compounding frequency. (If compounded annually, c=1. If monthly, c=12.)
The number of compounding periods, "n", is calculated with n=tc.
"t" is the time in years.
"c" is the compounding frequency.
In this problem:
t = 8
P = 12,000
r = 9%, or r = 0.09 for decimal form.
c = 365
Calculate "i" and "n".
i = r/c
i = 0.09/365
i = 0.00024657534
i ≈ 0.0002466
n = tc
n = 8(365)
n = 2920
Substitute these back into the formula:
A = P(1 + i)ⁿ
A = 12000(1+0.0002466)²⁹²⁰
A = 12000(1.0002466)²⁹²⁰
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