Quiz Rational Exponents

Question

Ise the compound interest formulas A = P

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and

A =Pe" to solve the problem given. Round answers to the nearest cent.

Find the accumulated value of an investment of $25,000 for 4 years at an interest rate of 4.5% if the money is a. compounded semiannually: b. compounded quarterly, c. compounded monthly, d. compounded continuously.

Answer 1

For parts a, b, and c, use the following formula: A = P(1 + r/n)^nt

c. A = 25000(1 + 0.045 / 12)¹²⁽⁴⁾ = 25000(1 + 0.00375)⁴⁸ = 25000(1.00375)⁴⁸ = $29920.36

Do parts a and b in a similar manner.

Answer 2

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

for 4 years, t=4, at 4.5% = .045=r,

n=number of times compounded annually

A=25000(1+.045)^4 for compounded once a year

= 25000(1.045)^4

for twice a year

A=25000(1.045/2)^8

for quarterly compounding

A=25000(1.045/4)^16

for monthly

A=25000(1.045/12)^48

for continuous compounding

A=25000e^.045(4)

= 25000e^.18