Question

Solve for the unknown number of years in each of the following: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present Value $400, $2091, $33105, $32800 Interest Rate 12%, 10%, 15%, 22% Future Value $1255, $3850, $388620, $202748

Answer 1

Present value = 400 and Future value = 1255 at a rate of 12%

We have Future value = Present value * ( 1 + r )ⁿ

= 400 * (1.12)ⁿ = 1255

(1.12)ⁿ = 1255 / 400 = 3.1375

Take log on both sides

n * Log (1.12) = Log (3.1375)

n * 0.049218 = 0.496584

n = 0.496584 / 0.049218 = 10.09 Years

Case - II

Present value = 2091, Future value = 3850 at 10%

2091 * (1.10 )ⁿ = 3850

(1.10 )ⁿ = 3850 / 2091 = 1.841224

n * Log (1.10) = Log (1.841224)

n * 0.041392685 =  0.26510663

n =  0.26510663 / 0.041392685 = 6.40 Years

Case - III

33105 ( 1.15)ⁿ = 388620

( 1.15)ⁿ = 388620 / 33105 =  11.73901223

n * Log (1.15) = Log ( 11.73901223)

n * 0.06069784 =  1.06963156

n = 1.06963156 / 0.06069784 = 17.62

Case - 4

32800 * ( 1.22)ⁿ = 202748

( 1.22)ⁿ = 202748 / 32800 = 6.18134146

n * Log (1.22) = Log (6.18134146)

n * 0.08635983= 0.791083

n = 0.791083 / 0.08635983

n = 9.16 Years