A savings account earns 8 interest If 1000 is invested how m

A savings account earns 8% interest. If $1000 is invested, how many years is it until each of the following amounts is on deposit?

a)1360

b)2720

c)4316

d)6848

Solution

amount = principal (1+r)ⁿ

A=P (1+r)ⁿ

A=1000(1+0.08)ⁿ

taking log both sides

log A= log 1000 + nlog 1.08

a) A=1360

log 1360 = log 1000 + nlog 1.08

7.22= 6.9 +n (0.077)

0.32/0.077= n

n=4.15 or 4 years

b)2720

log 2720 = log 1000 + nlog 1.08

7.9= 6.9 +n (0.077)]

1/0.077 =n

n=12.99 or 13 years

c)4316

log 4316 = log 1000 + nlog 1.08

8.37 = 6.9 +n (0.077)]

1.47/0.077=n

19.1 or 19 years

d)6848

log 6848= log 1000 + nlog 1.08

8.83 =6.9 +n (0.077)]

1.93/0.077 =n

n=25.1 or 25 years