To solve this problem, we need to find the equivalent payment in 2 months' time for two future payments, taking into account the time value of money using simple interest.

Formula for Simple Interest: The formula for calculating the future value with simple interest is:

$A = P(1 + rt)$

Where:

• $A$ is the amount (future value),
• $P$ is the principal (initial payment),
• $r$ is the interest rate per time period (annual rate),
• $t$ is the time in years.

We need to calculate the equivalent payment in 2 months for the two future payments:

1. $8,175 due in 12 months
2. $4,000 due in 21 months

We'll first calculate the equivalent of these two amounts in 2 months. Since the interest is simple, we can use the formula to find their present value relative to 2 months from now.

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Step 1: Equivalent Value of $8,175 due in 12 months

The time from 2 months to 12 months is 10 months, or $\frac{10}{12} = \frac{5}{6}$ years.

For this payment:

$A = 8,175(1 + 0.035 \times \frac{5}{6})$ $A = 8,175(1 + 0.029167)$ $A = 8,175 \times 1.029167$ $A = 8,419.71$

The equivalent amount in 2 months' time for the $8,175 payment due in 12 months is $8,419.71.

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Step 2: Equivalent Value of $4,000 due in 21 months

The time from 2 months to 21 months is 19 months, or $\frac{19}{12} \approx 1.5833$ years.

For this payment:

$A = 4,000(1 + 0.035 \times 1.5833)$ $A = 4,000(1 + 0.055417)$ $A = 4,000 \times 1.055417$ $A = 4,221.67$

The equivalent amount in 2 months' time for the $4,000 payment due in 21 months is $4,221.67.

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Step 3: Adding the Equivalent Values

Now, we'll add the equivalent values from the two future payments:

$8,419.71 + 4,221.67 = 12,641.38$

So, the equivalent payment in 2 months' time is $12,641.38.

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Final Answer:

The equivalent payment in 2 months' time would be $12,641.38.

Would you like further clarification or details on any part of the solution?

Related Questions:

1. How would the calculation change if the interest rate were compounded rather than simple?
2. How can you calculate the present value of multiple future payments with simple interest?
3. How would the interest rate affect the future value of payments over time?
4. What would the equivalent payment be if the interest rate were 5% instead of 3.5%?
5. How does the length of time between the payments affect the total equivalent amount?

Tip:

When dealing with simple interest, it's crucial to convert the time periods into years since the rate is typically given annually.