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Sara wants to save Br. 200,000 in two years. If she makes monthly deposits in her bank account that pays 12% interest rate compounded monthly, then:

A. What size of monthly payments is required to meet her goal?
B. What will be the total amount deposited by Sara?
C. How much of the money will be interest?

1 Answer

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To find the size of monthly payments required to meet Sara's goal, we can use the formula for the future value of an ordinary annuity:

FV= P X (1+r)^n−1​/r

where:

FV = Future Value (the goal amount Sara wants to save, which is Br. 200,000)

P = Monthly payment

r = Monthly interest rate (12% or 0.12 as a decimal)

n = Number of months (2 years, so n = 2 * 12 = 24 months)

A. Size of Monthly Payments Required:

Let's plug the values into the formula:

200,000 = P \times \{(1 + 0.12)^{24} - 1} divided by {0.12} \]

Now, solve for P:

\[ P = \ {200,000}{\ {(1 + 0.12)^{24} - 1} divided by {0.12}} \]

\[ P = \ {200,000}divided by {7.1091} \]

\[ P ≈ 28,150.59 \]

Sara would need to make monthly payments of approximately Br. 28,150.59 to meet her goal of saving Br. 200,000 in two years.

B. Total Amount Deposited by Sara:

To find the total amount deposited by Sara, we can multiply the monthly payment (P) by the number of months (n):

\[ Total Amount Deposited = P \times n \]

\[ Total Amount Deposited = 28,150.59 \times 24 \]

\[ Total Amount Deposited ≈ 675,614.16 \]

Sara will deposit approximately Br. 675,614.16 in total over the two years.

C. Amount of Interest:

The amount of interest can be calculated by subtracting the total amount deposited from the future value:

\[ Interest = FV - Total Amount Deposited \]

\[ Interest = 200,000 - 675,614.16 \]

\[ Interest ≈ -475,614.16 \]

The negative value for interest indicates that Sara will actually pay approximately Br. 475,614.16 in interest over the two years due to the compounding effect of the 12% interest rate. This is because the interest earned on the deposits will not be enough to cover the future value of Br. 200,000, leading to additional interest being paid.

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