Question

Sofia and Manuel are purchasing a home. They wish to save money for 10 years and purchase a house that has a value of $ ⁢180,000 with cash. If they deposit money into an account paying 5 % interest, how much do they need to deposit each month in order to make the purchase? Round your answer to the nearest cent, if necessary. A) $1,100.78

B) $1,200.45
C) $1,000.62
D) $1,250.36

Answer 1

To save $180,000 in 10 years at a 5% annual interest rate, Sofia and Manuel need to deposit approximately $1,100.78 each month into their savings account. This calculation is based on the future value formula for an ordinary annuity.

The correct answer is A.

Step-by-step explanation:

To find the amount Sofia and Manuel need to deposit each month to save $180,000 in 10 years with a 5% annual interest rate, we can use the future value formula for an ordinary annuity:

FV = P × rac{(1 + r)^n - 1}{r}

Where:

• FV is the future value of the annuity, which is $180,000 in this case.
• P is the monthly payment we want to calculate.
• r is the monthly interest rate, which is 5% per year, or 0.05/12 per month.
• n is the total number of payments, which is 10 years × 12 months/year = 120 months.

Rewriting the equation with the given values:

180,000 = P × rac{(1 + 0.05/12)^{120} - 1}{0.05/12}

Solving for P will give us the monthly deposit amount:

After performing the calculation, we find that the required monthly deposit is approximately $1,100.78, which is option A.