Question

uestion 1: a) what sum must be loaned at 8 % annual simple interest to earn 1,350 SR after 4 years? How long will it take from present value equal to 1,500 SR to future value equal to 2,025 SR with 5 % annual simple interest? c) How long will it take from present value equal to 1,500 SR to future value equal to 2,110.65 SR with 5 % annual compound interest?

Answer 1

a) formula of simple interest = prot where p = principal: r = interest rate (in decimal): t = time Therefore r = 8 % = 0.08: t = 4: p = ? Implies 1350 = p times 0.08 times 4 Implies p = 1350/4 times 0.08 = 4218.75 S R answer: 4218.75 S R b) P V = 1500 S R and F V = 2025 S R Therefore simple interest earned = F V - P V = 525 S R Therefore principle times r times t = 525 Implies 1500 times 0.05 times t = 525 Implies t = 525/1500 times 0.05 = 7 Therefore answer: 7 year c) the formula of compound interest Implies future value = present value (1 + r)_^t Implies 2110.65 = 1500 (1 + 0.05)^t Implies (1 + 0.05)^t = 2110.65/1500 = 1.4071 Implies (1.05)^t = 1.4071 taking logarithm on both sides Implies t log (1.05) = log (1.4071) Implies t = log(1.4071)/log (1.05) = 6.999 answer: 6.999 year