Question

At a growth (interest) rate of 8 percent annually, how long will it take for a sum to double? To triple? Use Appendix A for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

Answer 1

Answer:

n =   ㏒ P ÷ ㏒ (1.08)

Explanation:

Compound interest rate

A = P × $(1 + r)^{n}$

where

P = principal amount (the initial amount you borrow or deposit)

r  = annual rate of interest (as a decimal)

A = amount of money accumulated after n years, including interest.

n  =  number of years

Since we want the principle amount to double i.e., A = 2P

put this in above equation

2P = P × $(1 + r)^{n}$

divide both sides by P, we get

P = $(1 + r)^{n}$

put r = 0.08

P = $(1 + 0.08)^{n}$

P = $(1 .08)^{n}$

Taking log on both sides

㏒ P =㏒ $(1 .08)^{n}$

㏒ P = n ㏒ (1.08)

n =   ㏒ P ÷ ㏒ (1.08)