Question

Determine how long it will take for a principal amount of $13,000 to double its initial value when deposited into an account paying interest at a rate of 21.4 percent, continuously compounded.

Answer 1

Compound interest can be defined as the interest on a deposited amount, an investment that is compounded based on its principal and interest rate.

It will take about 3.239 years for the principal amount of $13,000 to double its initial value.

From the above question, we can deduce that we are to find the time "t"

The formula to find the time "t" in compound interest is given as:

t = ln(A/P) / r

where:

P = Principal = $13,000

R = Interest rate = 21.4%

A = Accumulated or final amount

From the question, the Amount "A" is said to be the double of the principla.

Hence,

A = $13,000 x 2

= $26,000

• Step 1: First, convert R as a percent to r as a decimal

r = R/100

r = 21.4/100

r = 0.214 per year.

• Step 2: Solve the equation for t

t = ln(A/P) / r

t = ln(26,000.00/13,000.00) / 0.214

t = 3.239 years

Therefore, it will take about 3.239 years for the principal amount of $13,000 to double its initial value.

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