The time taken for the amount to double is 14.2 years.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It is given that at the age of 4, Ted received an inheritance of $2,500. His mother invested the money in an account bearing 5% annual interest.
The formula for calculating the amount is given as:-
A = P ( r / 100 )[tex].^t[/tex]
Here, A is the total amount, P is the principal amount, r is the rate of interest and t is the time period.
The time in which the amount will become double is calculated as:-
A = P ( rate / 100 )[tex].^t[/tex]
2500 x 2 = 2500( 1.05)[tex].^t[/tex]
5000 / 2500 = ( 1.05)[tex].^t[/tex]
2 = ( 1.05)[tex].^t[/tex]
Take a log on both sides to calculate the value of t.
log ( 2 ) = log ( 1.05)[tex].^t[/tex]
log ( 2 ) = t log ( 1.05)
t = log ( 2 )/ log ( 1.05 )
t = 14.2
Hence, the time taken for the amount to double is 14.2 years.
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