Annual:

Semiannual:

Monthly:

Daily:

Continuously:

Annual:

Semiannual:

Monthly:

Daily:

Continuously:

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

Where P = principal amount (the initial amount you borrow or deposit)

r = annual rate of interest (as a decimal)

t = number of years the amount is deposited or borrowed for.

A = amount of money accumulated after n years, including interest.

n = number of times the interest is compounded per year

r = annual rate of interest (as a decimal)

t = number of years the amount is deposited or borrowed for.

A = amount of money accumulated after n years, including interest.

n = number of times the interest is compounded per year

Annual: n = 1

A = P(1 + (r/n)^{nt} = [($32,000)(1 + (0.09)/(1)]^{(1)(5)} = [($32,000)(1 + 0.09)]^{5} =
**$49,235.97**

Semiannual: n = 2

A = P(1 + (r/n)^{nt} = [($32,000)(1 + (0.09)/(2)]^{(2)(5)} = [($32,000)(1 + 0.045)]^{10} =
**$49,695.02**

Monthly: n = 12

A = P(1 + (r/n)^{nt} = [($32,000)(1 + (0.09)/(12)]^{(12)(5)} =
**$50,101.79**

Daily: n = 365 days (unless it's a leap year)

A = P(1 + (r/n)^{nt} = [($32,000)(1 + (0.09)/(365)]^{(365)(5)} = [($32,000)(1 + 2.466 x 10^{-4})]^{1825}

Continuous:

A = Pe^{rt }= ($32,000)e^{(0.09)(5)} = ($32,000)e^{0.45} =
**$50,185.99**

Semiannual: P(5) = 32000(1+0.09/2)^(2*5) = $49695.02

Monthly: P(5) = 32000(1+0.09/12)^(12*5) = $50101.79

Daily: P(5) = 32000(1+0.09/365)^(365*5) = $50183.21

Continuously: P(5) = 32000e^(5*0.09) = $50185.99

I assume you're having trouble with your interest rate formula, which is Interest= principle x rate x time.

Here's a different (longer) way to work the problem.

Start by finding out how much 9% of $32,000 (per every 12 months) works out to be.

(multiply $32,000 by 0.09, or 9% = x)

Interest rate will be added to the total dollar amount. Be sure that you ONLY add this full amount to the annual figure.

You can divide X (the amount of interest in dollars) by 12 months to find the monthly interest payment.

You can divide X (the amount of interest in dollars) by 6 months to find the semiannual payment.

Take care when you reach 'daily.' You'll need to change months to days, which should give you a pretty small (think decimals) number. ;-)

32000(1+.09/2)

32000(1+.09/12)

32000(1+.09/365)

32000e

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