Question

How long will it take $800 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places.

8%.

year(s)

12%.

year(s)

19%.

year(s)

100%.

year(s)

Answer #1

We use the formula:

A=P(1+r/100)^n

where

A=future value($1600)

P=present value

r=rate of interest

n=time period.

1.

1600=800(1.08)^n

(1600/800)=1.08^n

2=1.08^n

Taking log on both sides;

log 2=n*log 1.08

Hence n=log 2/log 1.08

which is equal to

**=9.01 years(Approx)**

**2.**

1600=800(1.12)^n

(1600/800)=1.12^n

2=1.12^n

Taking log on both sides;

log 2=n*log 1.12

Hence n=log 2/log 1.12

which is equal to

**=6.12 years(Approx)**

**3.**

1600=800(1.19)^n

(1600/800)=1.19^n

2=1.19^n

Taking log on both sides;

log 2=n*log 1.19

Hence n=log 2/log 1.19

which is equal to

**=3.98 years(Approx)**

**d.**

1600=800(1.2)^n

(1600/800)=1.2^n

2=1.2^n

Taking log on both sides;

log 2=n*log 1.2

Hence n=log 2/log 1.2

which is equal to

**=1 year.**

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