Answer:
6.5% at simple interest requires 30.77 years
6.0% at compounding of 6.5% requires 18.85 years
Explanation:
We want a PV of $1 to befome $3 in the future
[tex]1 (1 + r \times n) = 3\\(1 + 0.065 \times n) = 3\\n = (3 - 1) / 0.065[/tex]
n = 30,769
Compounding interest:
[tex](1+r)^n = 3\\log _{1+r}3 = n\\n = \frac{log 3}{log (1+r)} \\n = \frac{log 3}{log (1+0.06)}[/tex]
n = 18.85417668
n = 18.85
Answer:
Explanation:
To triple your balance( principal ) using simple interest rate
A = 3 * P = 3P (equation 1)
A = new amount
p = principal
T = x
R = interest rate = 6.5%
to calculate the interest rate = [tex]\frac{PTR}{100}[/tex] ( equation 2 )
note A = principal + interest rate
A = p + [tex]\frac{PTR}{100}[/tex] therefore A = p ( 1 + [tex]\frac{TR}{100}[/tex] ) ( equation 3 )
from (equation 1) A = 3P substitute this into (equation 3)
equation 3 becomes: 3P = P ( 1 + [tex]\frac{TR}{100}[/tex] ) divide both sides of the equation by P
equation becomes: 3 = ( 1 + [tex]\frac{T6.5}{100}[/tex] ) therefore 3 = 1 + 0.065T
hence T = [tex]\frac{3-1}{0.065}[/tex] = [tex]\frac{2}{0.065}[/tex] = 30.76 ≈ 31 years
To triple your balance using the compound interest
R = 6%
A = 3P
using the compound interest formula
A = P ( 1 + [tex]\frac{R}{100}[/tex])^t
3P = P ( 1 + [tex]\frac{6}{100}[/tex] )^t
3 = ( 1.06 )^t
t = [tex]\frac{log 3}{log 1.06}[/tex] = 18.85 years ≈ 19 years
