Answer:
15.7 years
Step-by-step 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.
