Compound Interest A deposit of $1000 is made in an account that earns interest at an annual rate of 5%. How long will it take for the balance to double when the interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously?
(a)
To calculate: The time required so that the deposited amount become double if the amount of
Given Information:
The amount of
Formula used:
The compound interest formula,
Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals, t is the number of years and n is the number of times compounded per year.
The property of logarithms for the expression
Calculation:
Consider that the amount of
Since, the principal amount deposit in the account is
The number of times compounded per year is
Now, the amount become double of the deposited amount after t years, then the amount after t years is
The rate of interest compounded annually is,
Substitute
(b)
To calculate: The time required so that the deposited amount become double if the amount of
(c)
To calculate: The time required so that the deposited amount become double if the amount of
(d)
To calculate: The time required so that the deposited amount become double if the amount of
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