Question

Find the term t of each continuously compounded account below rounded to the nearest tenth of a year. In the chart, B is the

ending balance, P is the principal, and r is the interest rate expressed as a percent.

Answer 1

The term, t of each continuously compounded account below rounded to the nearest tenth of a year are;

a. t = 3.0 years

b. t = 5.0 years

c. t = 3.1 years

d. t = 1.9 years

e. t = 5.0 years

What is the term, t?

a.

B = $2,124.00

P = $2,000.00

r = 2%

t = ln(B/P) / r

t = ln(2,124.00/2,000.00) / 0.02

t = 3.007696 years

t = 3.0 years

b.

B = $957.60

P = $900.00

r = 1.25%

t = ln(B/P) / r

t = ln(957.60/900.00) / 0.0125

t = 4.962831 years

t = 5.0 years

c.

B = $25,700.00

P = $25,000.00

r = 0.9%

t = ln(B/P) / r

t = ln(25,700.00/25,000.00) / 0.009

t = 3.068352 years

t = 3.1 years

d.

B = $185.50

P = $175.00

r = 3%

t = ln(B/P) / r

t = ln(185.50/175.00) / 0.03

t = 1.942297 years

t = 1.9 years

e.

B = $1,084,000.00

P = $1,000,000.00

r = 1.6%

t = ln(B/P) / r

t = ln(1,084,000.00/1,000,000.00) / 0.016

t = 5.041119 years

t = 5.0 years