Question

A savings account deposit of $150 is to earn 6.5% interest. After how many years will the investment be worth $450? Use y=a(1+r) and round to the nearest tenth.

a) 6.2 years
b) 7.3 years
c) 8.5 years
d) 9.8 years

Answer 1

To find the number of years it will take for the investment to be worth $450, we can use the formula for compound interest. Plugging the values into the formula, we can solve for t and determine the number of years. Rounding the answer to the nearest tenth, the investment will be worth $450 after approximately 1.4 years.

Step-by-step explanation:

To find the number of years it will take for the investment to be worth $450, we can use the formula for compound interest. The formula is y = a(1 + r)^t, where y is the future value, a is the initial deposit, r is the interest rate, and t is the number of years.

In this case, we have a = $150, y = $450, and r = 6.5%. Plugging these values into the formula, we get $450 = $150(1 + 0.065)^t.

Now we can solve for t. Dividing both sides of the equation by $150, we get 3 = (1 + 0.065)^t. To isolate the exponent, we can take the natural logarithm of both sides: ln(3) = t * ln(1 + 0.065). Using a calculator, we find that t is approximately 1.432 years.

Rounding this to the nearest tenth, the investment will be worth $450 after approximately 1.4 years. Therefore, the correct answer is option a) 6.2 years.