You have invested in a long-term, fixed deposit account earning 4% per year for 20 years, compounded annually. Your friend has invested in a similar account but one that earns 4.25% per year, compounded semi-annually. If each of you deposited $5,000, by what amount is your friend wealthier than you due to this deposit?
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A. B. C. D.C
The friend's account has 5,000*(1+0425/2)^40 = 11,595 at the end of 20 years. Your account has 5,000*(1.04^20) = 10,956. The difference is $639.
To determine the amount by which your friend is wealthier than you due to the deposit, we need to calculate the future value of each investment and compare the results.
For your investment: Principal amount (P) = $5,000 Interest rate (r) = 4% per year Number of years (n) = 20 Compounding frequency (m) = 1 (compounded annually)
The formula to calculate the future value (FV) of an investment with compound interest is: FV = P * (1 + r/m)^(n*m)
Using the values from your investment: FV = $5,000 * (1 + 0.04/1)^(20*1) FV = $5,000 * (1 + 0.04)^20 FV ≈ $5,000 * 1.04^20 FV ≈ $5,000 * 1.8385 FV ≈ $9,192.50
For your friend's investment: Principal amount (P) = $5,000 Interest rate (r) = 4.25% per year Number of years (n) = 20 Compounding frequency (m) = 2 (compounded semi-annually)
Using the values from your friend's investment: FV = $5,000 * (1 + 0.0425/2)^(20*2) FV = $5,000 * (1 + 0.02125)^40 FV ≈ $5,000 * 1.02125^40 FV ≈ $5,000 * 1.8750 FV ≈ $9,375.00
To find the difference in wealth between you and your friend, subtract the future value of your investment from the future value of your friend's investment: Difference = FV (friend) - FV (you) Difference = $9,375.00 - $9,192.50 Difference ≈ $182.50
Therefore, your friend is wealthier than you by approximately $182.50 due to this deposit.
None of the provided answer options match the calculated amount. The closest answer is $601 (Option B), but it does not correspond to the calculated difference.