Question 952474: Is this correct? Thanks in advance.
Question
A student knows that she will need $3,500 five years from now. She must decide between Bank A, which offers 7% compounded weekly, and Bank B, which offers 6% compounded continuously. Which bank should she use? Explain your answer.
My answer:
Bank A
A=P(1+r)^n
3500=P(1+0.0013)^260
P=(5500)/(1+0.0013)^260
P=(3500)/(1.0013)^260
P=3500/1.4018
P=$2496.79
Bank B
A=Pe^ri
3500=Pe^0.06(5)
P=3500/e^0.06(5)
P=3500/2.71828^0.3
P=3500/1.3498585
P=$2592.86
She should use Bank A because she will invest less.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Bank A's formula in your solution is not correct but Bank A is still correct choice since principal is still less
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Bank A
A = P(1+(r/n))^tn where P is the principal, r is interest rate, n is the number of times the interest rate is compounded, t is time in years, therefore
3500 = P*(1+(.07/52))^(5*52)
3500 = P*(1.418733588)
P = 3500/(1.418733588) = 2466.988890308 approx $2466.99
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Bank B
A = Pe^rt, where P is principal, r is annual interest rate, t is time in years
3500 = Pe^(.06*5)
3500 = P*2.71828^(.30) = P*(1.349858535)
P = 3500 / (1.349858535) = 2592.864295615 approx $2492.86
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Bank A requires her to invest less
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