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Problem 5-41 1. Find the FV of $1,500 invested to earn 15% after 5 years. c. Find the PV of $1,500 due in 5 years if the discount rate is 5 114. A security has a cost of $1,500 and will return $2.000 after 10 years. What rate of return does the security provide 15. Suppose California's population is 38.5 million people, and its population is expected to grow by 296 annually. How long will it take for the population to double? 19 L Find the PV of an ordinary annuity that pays $2,000 each of the next 10 years in the interest rate 20 is 10%. Then find the FV of that same annuity. 23 E How will the PV and FV of the annuity change if it is an annuity due rather than an ordinary 24 27 L Find the annual payments for an ordinary annuity and an annuity due for 10 years with a PV of $1,500 and an interest rate of 1096

Answer 1

(a) Present Value = PV = $1500

Number of years = n = 5

Interest Rate = r = 15%

Future Value = FV = PV(1+r)ⁿ = 1500(1+0.15)⁵ = $3017.04

(c) Future Value = FV = $1500

Number of years = n = 5

Interest Rate = r = 5%

Let Present Value be PV

Future Value = FV = PV(1+r)ⁿ

=> PV = FV/(1+r)ⁿ

= 1500/(1+0.05)⁵ = $1175.29

(d) Present Value = PV = $1500

Future Value = FV = 2000

Number of years = n = 10

Let rate of return be r

FV = PV(1+r)ⁿ

=> r = (FV/PV)^1/n - 1 = (2000/1500)^1/10 - 1 = 0.0292 or 2.92%

(e) Present Population = P = 38.5 million

To double, Future Population = F = 2*P = 2*38.5 = 77 million

Growth = r = 2%

Let the number of years be n

=> F = P(1+r)n

=> n = ln (F/P) / ln (1+r) = ln (77/38.5) / ln (1+0.02) = 35 years