Question

A person invests 1500 dollars in a bank. The bank pays 4% interest compounded

annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 1800 dollars?

Answer 1

4.6 years

Explanation:

We are to calculate the time in years.

The formula is given as:

t = ln(A/P) / n[ln(1 + r/n)]

Where:

A = Amount after t years = 1800

P = Initial Amount invested = 1500

r = Interest rate = 4%

n = Frequency at which the interest was compounded = Annually = 1

First, convert R percent to r a decimal

r = R/100

r = 4%/100

r = 0.04 per year,

Then, solve our equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(1,800.00/1,500.00) / ( 1 × [ln(1 + 0.04/1)] )

t = 4.649 years

Approximately = 4.6 years