Question

You can afford monthly deposits of $190 into an account that pays 3.3% compounded monthly. How long will it be until you have $8,900 to buy a​ boat?

Type the number of​ months: _________

​(Round to the​ next-higher month if not​ exact.)

Answer 1

To reach $8,900 with monthly deposits of $190 at 3.3% interest compounded monthly, it will take approximately 177 months when rounded to the next higher month.

Step-by-step explanation:

To determine how long it will take to save $8,900 with monthly deposits of $190 at an annual interest rate of 3.3% compounded monthly, we use the future value of a series formula for compound interest:

FV = P × ((1 + r)^n - 1) / r

Where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of months. The monthly interest rate is calculated as the annual rate divided by 12.

Since r is 3.3% annually, the monthly interest rate r is:

3.3% / 12 = 0.275% or 0.00275 in decimal form.

Now we have to find n such that:

FV = 8900

P = 190

r = 0.00275

Substituting these values in the above formula gives us:

8900 = 190 × ((1 + 0.00275)^n - 1) / 0.00275

Using a financial calculator or an algebraic method, we find that the value of n which satisfies this equation is approximately 176.6 months. Since we need to round to the next higher month if not exact, the answer is 177 months.