Hello, I'm having a hard time fingering our this question. Not really sure what formula to use. Thanks in advance!
For a five year period, Ned deposited $800 each quarter into an account paying 5.6% annual interest compounded quarterly.
(a) How much money was in the account at the end of 5 years?
(b) How much interest was earned during the 5 year period?
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A is the future value of the investment
P is the principal amount (the initial deposit)
r is the annual interest rate
n is the number of times interest is compounded per year
t is the number of years
In this case, we have:
P = $800 (since that's the quarterly deposit)
r = 5.6% (or 0.056 as a decimal)
n = 4 (since interest is compounded quarterly)
t = 5 (since we're looking at a 5-year period)
(a) To find the total amount of money in the account at the end of 5 years, we can substitute the values into the formula:
A = 800(1 + 0.056/4)^(4*5)
Calculating this, we get:
A ≈ $6,422.25
So, the amount of money in the account at the end of 5 years is approximately $6,422.25.
(b) To calculate the interest earned during the 5-year period, we can subtract the initial deposit (P) from the final amount (A):
Interest = A - P
Interest = $6,422.25 - ($800 * 4 * 5)
Calculating this, we get:
Interest ≈ $2,622.25
Therefore, the amount of interest earned during the 5-year period is approximately $2,622.25.