Question

In: Economics

The officers and board of directors of the Philippine Society of Mechanical Engineers desires to award...

The officers and board of directors of the Philippine Society of Mechanical Engineers desires to award a P3,600.00, scholarship annually to deserving mechanical engineering students for as long as its scholarship fund shall last. The fund was started July l, 1987, by a donor in the amount of P18,000.00 The Philippine Society of Mechanical Engineers invested this sum at that time at 8% per annum and plans on adding P600.00 each year to the fund from its dues starting July 1, 1988 for as long as award are made. For how many years starting July 1, 1988 can scholarship be awarded? And What will be the balance in the fund after the last award is made?

Expert Solution

Let us assume the scholarship will be awarded for n years.

The present value of payment must be equal to the present value of deposit.

The present value of payments will be

The present value of deposit will be expressed as

These two factors must be equal

Taking log on both sides we get

Thus, the number of payments would be 8.

After the last payment the balance would be

The present value of 8 years = 760.08

Amount left in account = 760.08 × 1.08^8 = 1,406.86

Alternative method

Rahul Sunny answered 2 years ago

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