1 At what annual rate of interest will 1000 have to be inves

1. At what annual rate of interest will $1000 have to be invested to amount to $2500 in 10 years?

2. Evaluate the followings using change of base formula with base 10 or e. (Express as a decimal form)

Solution

1. Let the annual rate of interest be r %. Since the question does not mention compounding, we will assume that there is simple rate of interest. Then interest on $ 1000 for 10 years at r % p.a. = 1000*10 * r/100 = 100r. Then 1000 + 100r = 2500. Therefore, 100r = 2500 - 1000 = 1500 so that r = 15. The answer is 15 %.

2. We know that log_b x = log_d x / log_d (b)

(1) Here b = 4, and ( say) d = 10. Then log₄ 23= log ₁₀ 23/ log₁₀ (4) = 1.361728/0.60206 = 2.26 (approx).

(2) Here, b = 3 and ( say) d = 10. Then log₃ ( o.1483) = log ₁₀ ( 0.1483)/ log₁₀ ( 3 ) = -0.828856/ 0.477121= - 1.737 = - 1.74 ( approx).