Question

Waiting period. Jamal is waiting to be a millionaire. He wants to know how long he must wait if a. he invests $25.947.68 at 18% today? b. he invests $49.449.44 at 13% today? C. he invests $151,683.62 at 11% today? d. he invests $302,109.37 at 6% today?

Answer 1

Answer to Part a.

Future Value = $1,000,000
Present Value = $25,947.68
Rate(r) = 18%
Time (n) = ??

Future Value = Present Value * (1 + r)^ n
$1,000,000 = $25,947.68 * (1 + 0.18)^n
$1,000,000 = $25,947.68 * 1.18^n
38.53909 = 1.18 ^n
ln(38.53909) = ln(1.18)
n = 22.06

Therefore, Jamal should invest for 22.06 years to be millionaire.

Answer to Part b.

Future Value = $1,000,000
Present Value = $49,449.44
Rate(r) = 13%
Time (n) = ??

Future Value = Present Value * (1 + r)^ n
$1,000,000 = $49,449.44 * (1 + 0.13)^n
$1,000,000 = $49,449.44 * 1.13^n
20.22268 = 1.13 ^n
ln(20.22268) = ln(1.13)
n = 24.60

Therefore, Jamal should invest for 24.60 years to be millionaire.

Answer to Part c.

Future Value = $1,000,000
Present Value = $151,683.62
Rate(r) = 11%
Time (n) = ??

Future Value = Present Value * (1 + r)^ n
$1,000,000 = $151,683.62 * (1 + 0.11)^n
$1,000,000 = $151,683.62 * 1.11^n
6.59267 = 1.11 ^n
ln(6.59267) = ln(1.11)
n = 18.07

Therefore, Jamal should invest for 18.07 years to be millionaire.

Answer to Part d.

Future Value = $1,000,000
Present Value = $302,109.37
Rate(r) = 6%
Time (n) = ??

Future Value = Present Value * (1 + r)^ n
$1,000,000 = $302,109.37 * (1 + 0.06)^n
$1,000,000 = $302,109.37 * 1.06^n
3.31006 = 1.06 ^n
ln(3.31006) = ln(1.06)
n = 20.54

Therefore, Jamal should invest for 20.54 years to be millionaire.