Question

Problem 8: Suppose that the nominal interest rate is 9 percent compounded monthly. We want to compare $10,000 received today to $15,000 received in 5 years. (a) (3 pts.) What is the future value of the amount received today (S)? (b) (2 pts.) What is the nominal interest rate (percent) at which the amount received today would increase to the amount being offered in the future? (be accurate to at least two decimal places)

Answer 1

Compound in treat formula (including principal) A - p(1 + r/n)^nt where A rightarrow amount P rightarrow interest rate t rightarrow time in years: n rightarrow no of time per year is compared p = $10, 000 t = 5 years r = 9% n = 12 (compounded monthly) A = 9000(1 + 0.09/12)^(12) (5) A = 9000(1 + 0.0075)^60 A = 9000(1.0075)^60 A = 140.91 .12 future value of amount received today is $14091.12 A = $15000 (amount received in future) p = $10, 000)amount received in future n = 12: t = 5 r = ? implies A = p(1 + r/n)^nt implies 15000 = 10, 000 (1 + r/12)6(12) (5) implies (15000/10000) = (1 + r/12)^60 implies 1.5 = (1 + r/12)^60 implies (1.5)^1/60 = [(1 + r/12)^60[^1/60 implies 1.00678 = 1 + r/12 \r\n 1 + r/12 = 1.00678 r/12 = (1.00678 - 1) r/12 = 0.00678 r = (0.00678) (12)r = 0.08136 r = 8.14