Sadie is saving for a new car. Below is the total amount of money in her savings account on the last day of each month. Show all
steps to find the mean amount of money Sadie saves each month. Round your answers to the nearest cent.
1 answer:
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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