20. I need your help! I have $15,000 that I can deposit in the Bank of Pandora a
ID: 2657192 • Letter: 2
Question
20. I need your help! I have $15,000 that I can deposit in the Bank of Pandora and earn 4% interest rate compounded semi-annually or in the Bank of Titanic and earn 4% interest rate compounded continuously. If I can keep the deposit for 5 years, where should I deposit? By how much is this amount higher than if I deposited in the other bank? A) Bank of Pandora, $32 B) Bank of Titanic, $36 C) Bank of Titanic, $27 D) Doesn’t matter where as I am receiving the same interest rate and investing for the same period of time
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Explanation / Answer
You deposit in Bank of Titanic, as interest is compounded more here.
Future value of an amount can be computed as -
FV = Amount x (1 + r)n
where, r = periodic rate of interest, n = no. of time periods
In case of Bank of Pandora, future value of deposit amount would be -
r = 4% / 2 = 2%, n = 5 x 2 = 10
FV = $15000 x (1 + 2%)10 = $18,285
In case of Bank of Titanic, since interest is compounded continuously, its future value will be -
r = 4%, n = 5
FV = Amount x e r x n = $15000 x e 0.04 x 5 = $15000 x e0.2 = $15000 x 1.2214 = $18,321
Amount is higher by = $18,321 - $18,285 = $36
Therefore, Option B is correct.
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