Asked by Junior Aleman on May 19, 2024
Verified
Simon Fraser recently received a $20 million donation to be used for scholarship purposes. If interest can be earned at 4.2% compounded monthly, determine the semi-annual amount of scholarships that students can apply for.
A) $423,692.20
B) $428,550.12
C) $431,084.45
D) $441,289.72
E) $444,821.94
Semi-annual Scholarships
Scholarships awarded twice a year, often to support the educational expenses of students.
- Familiarize oneself with the notion of perpetuity and how to ascertain payments for perpetuities.
- Acquire knowledge about the effects of various compounding schedules (monthly, quarterly, semi-annually, and annually) on future value and payments.
- Evaluate the financial outcomes associated with diverse interest rates and time frames of investment on scenarios involving savings and loans.
Verified Answer
JS
Jasmir Saint LouisMay 21, 2024
Final Answer :
A
Explanation :
To find the semi-annual scholarship amount, we use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount, P is the principal amount ($20 million), r is the annual interest rate (4.2% or 0.042), n is the number of times the interest is compounded per year (12 for monthly), and t is the time in years. Since we're looking for a semi-annual scholarship amount, t = 0.5 years. Plugging in the values: A = 20,000,000(1 + 0.042/12)^(12*0.5). Solving this gives approximately $20,423,692.20. The semi-annual scholarship amount is the interest earned over 6 months, which is $20,423,692.20 - $20,000,000 = $423,692.20.
Learning Objectives
- Familiarize oneself with the notion of perpetuity and how to ascertain payments for perpetuities.
- Acquire knowledge about the effects of various compounding schedules (monthly, quarterly, semi-annually, and annually) on future value and payments.
- Evaluate the financial outcomes associated with diverse interest rates and time frames of investment on scenarios involving savings and loans.
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