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5400 = 4800(1 + (r)/(365))^((365)(6))\n5400/4800 = 4800(1 + (r)/(365))^((365)(6))/4800\n1.125 = (1 + (r)/(365))^(2190)\n\sqrt[2190]{1.125} = \sqrt[2190]{ (1 + (r)/(365))^(2190)} \n1.0000537836544 = 1 + (r)/(365) \n1.0000537836544 -1 = 1 + (r)/(365) -1\n.0000537836544 = (r)/(365)\n(.0000537836544)(365) = ( (r)/(365))(365)\n.019631 = r

shagosd111 shagosd111 · Answer 2 · 2024-12-11T02:44:35-05:00

Answer:

the interest rate required in order for Josiah to end up with $5,400, assuming the interest is compounded daily, is 10.3%

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^nt

Where:

A = the amount of money in the account after the interest has been added

P = the initial investment (principal) of $4,800

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the money is left in the account

We know that A = $5,400 and t = 6 years, so we can substitute these values into the formula:

5400 = 4800(1 + r/n)^(6n)

To find the interest rate, we need to solve for r.

we know that the interest is compounded daily, so we will use n = 365

5400 = 4800(1 + r/365)^(6*365)

To find the interest rate, we need to solve for r, we can use a calculator to find the value of r.

r ≈ 0.103 or 10.3% to the nearest tenth of a percent

So, the interest rate required in order for Josiah to end up with $5,400, assuming the interest is compounded daily, is 10.3%