A condominium building needs to save $50,000 in 8 years with a savings account that yields 3.75% interest. What are the required quarterly payments?

To determine the required quarterly payments to accumulate $50,000 in 8 years with an account that yields 3.75% interest, it is important to use the future value of an annuity formula. In this context, the future value of an annuity considers a series of equal payments made at regular intervals, compounded at a specific interest rate.

Given that the interest rate is 3.75% annually, when breaking it down into quarterly payments, the effective rate per quarter becomes 3.75% divided by 4, which equals approximately 0.9375%. Over the course of 8 years, with 4 quarters per year, there are a total of 32 quarters.

Using the future value of an annuity formula:

[

FV = P \times \frac{(1 + r)^n - 1}{r}

]

where:

• (FV) is the future value ($50,000),

• (P) is the quarterly payment we want to find,

• (r) is the interest rate per quarter (0.9375% or 0.009375 as a decimal),

• (n) is the total number of payments (32 quarters).

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