23.03.2023 - 13:43

You want to buy a house within 3 years, and you are currently saving for the down payment. You plan to save $5,000 at the end of the first year, and you anticipate your annual savings will increase by

Question:

You want to buy a house within 3 years, and you are currently saving for the down payment. You plan to save $5,000 at the end of the first year, and you anticipate your annual savings will increase by 10% annually thereafter. Your expected annual return is 7%. How much will you have for a down payment at the end of year 3?

Answers (1)
  • g0rlum
    April 4, 2023 в 00:39

    To calculate the down payment at the end of year 3, we need to calculate the savings for each year and compound them.

    In the first year, you plan to save $5,000.

    In the second year, your savings will increase by 10%, so you will save 1.10*$5,000 = $5,500.

    In the third year, your savings will increase by another 10%, so you will save 1.10*$5,500 = $6,050.

    Now we need to compound these savings with the expected annual return of 7%. We can use the formula for compound interest:

    Final amount = Principal * (1 + (annual interest rate / n))^(n * time period)

    Where:

    • Principal is the initial amount of savings
    • Annual interest rate is the expected annual return
    • n is the number of \times the interest is compounded per year (in our case, it's once per year)
    • Time period is the number of years

    Using this formula, we can calculate the total savings at the end of year 3:

    Year 1 savings: $5,000 Year 2 savings: $5,500 Year 3 savings: $6,050

    Total savings at the end of year 3: = $5,000 * (1 + (0.07/1))^(1 * 3) + $5,500 * (1 + (0.07/1))^(1 * 2) + $6,050 * (1 + (0.07/1))^(1 * 1) = $16,391.57

    Therefore, at the end of year 3, you will have $16,391.57 for a down payment.

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