Calculate the accumulated amount of end-of-quarter payments of $10,000 made at 5.30% compounded monthly for 7 years.
To calculate the accumulated amount of the end-of-quarter payments, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t),
where:
A is the accumulated amount,
P is the principal amount (payment),
r is the annual interest rate (in decimal form),
n is the number of times interest is compounded per year, and
t is the number of years.
In this case, the principal amount (payment) is $10,000, the annual interest rate is 5.30% (or 0.053 in decimal form), the interest is compounded monthly (which means n = 12 times per year), and the number of years is 7.
Using these values, we can calculate the accumulated amount (A):
A = 10000(1 + 0.053/12)^(12*7).
Let's simplify and calculate the result step by step:
Step 1: Calculate the monthly interest rate:
r/n = 0.053/12 = 0.0044167.
Step 2: Calculate the exponent term:
n*t = 12 * 7 = 84.
Step 3: Calculate the accumulated amount:
A = 10000(1 + 0.0044167)^84.
Calculating this in a calculator or a spreadsheet, we find the accumulated amount:
A ≈ $14,983.05.
Therefore, the accumulated amount of the end-of-quarter payments of $10,000 made at 5.30% compounded monthly for 7 years is approximately $14,983.05.