Identify the choice that best completes the statement or answers the question. A

Question

Identify the choice that best completes the statement or answers the question. An initial deposit of $600 earns 3% interest, compounded quarterly. How much will be in the account in 10 years? Round to the nearest penny. a. $1, 083.67 b. $808, 71 c. $809.01 d. $1, 957.22 e. $646.55 2. How much more interest could $700 earn in 4 years, compounded semiannually (two times a year) if the annual interest rate were 3% instead of 2%? Assume that there are no deposits or withdrawals and round to the nearest penny. a. $14.62 b. $30.74 c. $42.29 d. $66.58 e. $30.55 3. What does the expression log 7^7^x equal? a. 10 b. x c. 0 d. 1 e. 7 Find the value of x. log_3 6, 561 = x a. x = 6, 561 b. x = 3 c. x = 8 d. x = 3, 281

Explanation / Answer

The formula for compound interest is F =P(1+r/n)nt, where P is the principal, F is the future value, r is the rate of interest, t is the number of years and n is the number of times, the interest is compounded in an year. Here, P= $ 600, r = 3/100, n = 4 and t=10. Hence, F = 600(1+3/400)10*4 = 600(403/400)40 = 600*1.348348612 = $ 809.01 ( on rounding off to the nearest penny/cent). Option (c ) is the correct answer. The required difference of interest is 700(1+3/200)8 – 700[(1+2/200)8 = 700[(203/200)8-(202/200)8] = 700(1.126492587-1.082856706) = 700*0.043635881 = $30.55(on rounding off to the nearest penny/cent). Option (e ) is the correct answer. log7(7x) = x. Option (b ) is the correct answer. log3 6561 =x or, x = log3(38). Hence, x = 8.Option (c ) is the correct answer.

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