Question

A person invests 3000 dollars in a bank. The bank pays 5.75% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 7200 dollars?

Answer 1

15.7 years

Explanation:

Use the formula for compound interest. A = P(1 + i)ⁿ

A is the total amount of money. A = 7200

P is the principal, starting money. P = 3000

i is the interest per compounding period in decimal form. Since interest is compounded annually, i = 0.0575

n is the number of compounding periods. n = ?

Substitute the information into the formula and isolate n.

A = P(1 + i)ⁿ

7200 = 3000(1 + 0.0575)ⁿ Solve inside the brackets

7200 = 3000(1.0575)ⁿ

7200/3000 = 1.0575ⁿ Divide both sides by 3000

2.4 = 1.0575ⁿ

n = (㏒ ans) / (㏒ base)

n = (㏒ (2.4)) / (㏒ (1.0575))

n = 15.659..... Exact answer

n ≈ 15.7 Rounded to the nearest tenth of a year

Therefore the person must leave the money in the bank for 15.7 years until it reaches 7200 dollars.