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Chapter 11: Q. 474 (page 1069)

Jacob invests $14,000in an account that compounds interest quarterly and earns 4%. How long will it take for his money to double?

Short Answer

Expert verified

The time taken to double the Jacob money is 17.4years.

Step by step solution

01

Step 1. Given Information 

We are given that Jacob invests $14,000and earns 4%interest quarterly.

02

Step 2. Formula for calculating compound interest

The formula for calculating compound interest is,

A=P1+rnnt

03

Step 3. Finding the time

Putting the values,

P=14,000r=0.04A=28,000n=4

28000=140001+0.0444t2800014000=(1+0.01)4t1.014t=2

04

Step 4. Taking logarithm 

Taking logarithm on both sides, we get

log(1.01)4t=log24tlog(1.01)=log2t=log24log(1.01)t=17.4151t鈮�17.4

It will take17.4years to double the money.

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