The owner of Oak Hill Squirrel Farm deposits $1,000 at the end of each quarter into an account paying 1.5% compounded quarterly. What is the value at the end of 8 years, 6 months? (Round your answer to the nearest cent.)
don't you have a handy annuity formula?
I am not sure how to calculate the 8 years and 6 months.
Interest is applied quarterly, so over 8 years, it's applied 8 × 4 = 32 times.
Over the remaining 6 months, it's applied 2 more times because a quarter of a year is 3 months.
So we have 8 x 4 + 2 = 34 interest periods altogether.
To calculate the value at the end of 8 years, 6 months, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A is the final amount,
P is the principal amount (initial deposit),
r is the annual interest rate (as a decimal),
n is the number of times the interest is compounded per year,
t is the number of years.
In this case, the principal amount is $1,000, the annual interest rate is 1.5% (or 0.015 as a decimal), the interest is compounded quarterly (so n = 4), and the time in years is 8.5 (8 years plus 6 months).
Plug in these values into the formula and calculate the final amount A:
A = 1000(1 + 0.015/4)^(4 * 8.5)
Using a calculator, simplify the expression inside the parentheses first:
(1 + 0.015/4) = 1.00375
Then, compute the exponent:
(1.00375)^(4 * 8.5) ≈ 1.41898
Finally, multiply the principal amount by the result:
A ≈ 1000 * 1.41898 ≈ $1418.98.
Therefore, the value at the end of 8 years, 6 months would be approximately $1418.98.