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If 32000 dollars is invested at an interest rate of 9 percent per year, find the value of the investment at the end of 5 years for the following compounding met

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4 Answers

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 
 
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
A = $50,183.21
 
Continuous:
 
A = Pert = ($32,000)e(0.09)(5) = ($32,000)e0.45 = $50,185.99

Annual: P(5) = 32000(1+0.09)^5 = $49235.97
 
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)5                   =49235.96656
32000(1+.09/2)10            =49695.0215
32000(1+.09/12)60          =50101.79286
32000(1+.09/365)(5×365)=50183.20618  This is the only one I'm not sure of.
32000e(.09×5)                   =50185.98994