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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

Annual:

Semiannual:

Monthly:

Daily:

Continuously:

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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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

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
Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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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

Jessica S. | Highly Effective Teacher Seeks to Create Life-Long LearnersHighly Effective Teacher Seeks to Create...
5.0 5.0 (50 lesson ratings) (50)
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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. ;-)
Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (6 lesson ratings) (6)
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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