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[SOWHAT0819]

You wish to set up a special fund by making uniform semiannual end-of-period deposits for 12 years. The fund will provide P350,000 at the end of each of the last five years of the 12-year period. If interest is 14% compounded semiannually, what is the required semiannual deposit to be made?

 

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To find the required semiannual deposit, we need to use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r,

where:
FV = future value
P = semiannual deposit
r = interest rate per period
n = number of periods

In this case, we have:
FV = P350,000 (the desired future value)
r = 14% compounded semiannually, which means the interest rate per period is 14% / 2 = 7%
n = 5 (since we want the fund to provide P350,000 at the end of each of the last five years)

Let's substitute these values into the formula and solve for P:

P350,000 = P * ((1 + 0.07)^5 - 1) / 0.07.

Simplifying this equation, we get:

P350,000 = P * (1.07^5 - 1) / 0.07.

Now, let's solve for P:

P350,000 * 0.07 = P * (1.07^5 - 1),
P24,500 = P * (1.07^5 - 1),
P = P24,500 / (1.07^5 - 1).

Using a calculator, we find:

P = P24,500 / (1.07^5 - 1) ≈ P4,442.20.

Therefore, the required semiannual deposit to be made is approximately P4,442.20.