Exponential Equations in Financial Contexts — Quiz
Question 4 • Financial Math
A certificate of deposit that compounds interest daily, or 365 times a year, has an advertised annual interest rate of 2.75% The advertisement also promises a final balance of $25,346.11 on an investment of $25,000 Which equation can be used to find the length of time in years of the investment?
Answer
A
25 comma 000 is equal to 25 comma 346 point 1 1 times open paren 1 plus 0 point 0 2 7 5 over 365 close paren to the t th power
B
25 comma 000 is equal to 25 comma 346 point 1 1 times open paren 1 plus 0 point 0 2 7 5 over 365 close paren to the t th power
C
25 comma 346 point 1 1 is equal to 25 comma 000 times open paren 1 plus 0 point 0 2 7 5 over 365 close paren raised to the 365 t power
D
25 comma 000 is equal to 25 comma 346 point 1 1 times open paren 1 plus 0 point 0 2 7 5 over 365 close paren raised to the 365 t power
Explanation
Use the compound-interest formula A = P(1 + r/n)^(nt), where P is the starting investment, A is the final balance, r is the annual rate, and n is the number of compounding periods per year. Substituting gives 25,346.11 = 25,000(1 + 0.0275/365)^(365t), so choice C has the correct amounts and exponent for daily compounding.
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