Question

find the balance for each compounding period on $50,000 for 2 1/2 years at a rate of 1.3% for quarterly, monthly, daily, hourly, countinuously

Answer 1

The balance for each compounding period on $50,000 for 2 1/2 down arrow years at a rate of 1.3% for Annually is approximately $51516.67, Semiannually is approximately $51528.04, Quarterly is approximately $51538.39, Monthly is approximately $51545.41, Daily is approximately $51546.33, Hourly is approximately $51546.58, Continuously is approximately $51546.81,

To find the balance for each compounding period on $50,000 for 2 1/2 years at a rate of 1.3%, we can use the compound interest formula:

`\[A = P \left(1 + (r)/(n)\right)^(nt),\]`

where:

- A is the future value of the investment,

- P is the principal amount (initial investment),

- r is the annual interest rate (as a decimal),

- n is the number of times interest is compounded per year,

- t is the time the money is invested for in years.

a. Annually (compounded once per year):

`\[A = 50000 \left(1 + (0.013)/(1)\right)^(1 * 2.5) \approx \$51516.67.\]`

b. Semiannually (compounded twice per year):

`\[A = 50000 \left(1 + (0.013)/(2)\right)^(2 * 2.5) \approx \$51528.04.\]`

c. Quarterly (compounded four times per year):

`\[A = 50000 \left(1 + (0.013)/(4)\right)^(4 * 2.5) \approx \$51538.39.\]`

d. Monthly (compounded twelve times per year):

`\[A = 50000 \left(1 + (0.013)/(12)\right)^(12 * 2.5) \approx \$51545.41.\]`

e. Daily (compounded 365 times per year):

`\[A = 50000 \left(1 + (0.013)/(365)\right)^(365 * 2.5) \approx \$51546.33.\]`

f. Hourly (compounded 8,760 times per year):

`\[A = 50000 \left(1 + (0.013)/(8760)\right)^(8760 * 2.5) \approx \$51546.58.\]`

g. Continuously:

`\[A = 50000e^(0.013 * 2.5) \approx \$51546.81.\]`

In summary, the balance for each compounding period for the given investment varies, with continuous compounding yielding the highest balance of approximately $51546.81.

The probable question may be:

Find the balance for each compounding period on $50,000 for 2 1/2 down arrow years at a rate of 1.3%.

a. Annually

b. Semiannually

c. Quarterly

d. Monthly

e. Daily

f. Hourly

g. Continuously