Question

mohal is going to invest $2,100 and leave it in an account for 16 years. assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for mohal to end up with $3,300?

Answer 1

To find the interest rate required for Mohal to end up with $3,300 in 16 years with daily compounding, we can use the formula for compound interest. By solving the equation and using logarithms, the interest rate is approximately 3.42%.

Step-by-step explanation:

To find the interest rate required for Mohal to end up with $3,300, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Given that Mohal is investing $2,100 for 16 years and wants to end up with $3,300, we can plug in the values to solve for r.

$3,300 = $2,100(1 + r/365)^(365*16)

Simplifying, we get: (1 + r/365)^(5,840) = 3,300/2,100 = 11/7

Now, we can use logarithms to solve for r:

1. Take the natural logarithm of both sides: ln((1 + r/365)^(5,840)) = ln(11/7)
2. Apply the power rule of logarithms to bring the exponent down: 5,840ln(1 + r/365) = ln(11/7)
3. Divide both sides by 5,840: ln(1 + r/365) = ln(11/7) / 5,840
4. Take the antilogarithm of both sides: 1 + r/365 = e^(ln(11/7) / 5,840)
5. Subtract 1 from both sides: r/365 = e^(ln(11/7) / 5,840) - 1
6. Multiply both sides by 365: r = 365(e^(ln(11/7) / 5,840) - 1)

Plugging in the values, the interest rate required for Mohal to end up with $3,300 is approximately 0.0342 or 3.42%.