Question

About how long will it take $1 to grow to $10 if the interest rate is 6.3% CIM(monthly compounding)?

Answer 1

Given,

Present value = $1

Future value = $10

Interest rate = 6.3% or 0.063

Solution :-

Monthly interest rate (r) = 0.063 x 1/12 = 0.00525

Let no. of months be 'n'

Future value = Present value x (1 + r)ⁿ

$10 = $1 x (1 + 0.00525)ⁿ

$10/$1 = (1.00525)ⁿ

$10 = (1.00525)ⁿ

Taking 'Log' both sides,

Log(10) = Log(1.00525)ⁿ

Log(10) = n.Log(1.00525)

2.302585093 = n.(0.0052362668)

2.302585093 0.0052362668 = n

439.737924163 = n

So,

No. of years = n 12 months

= 439.737924163 12 months = 36.64 years

Thus, it will take 36.64 years to grow $1 to $10