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What is the future value (as of 10 years from now) of an annuity that makes 10 annual payments
of P5,000, if the interest rate is 7% per year compounded quarterly?
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My understanding is that they want to find future value of the ordinary annuity saving plan
in 10 years from now, given that a person makes 10 deposits of P5000 each at the end of each
of 10 years. The interest rate in the bank is 7% per year compounded quarterly.
The complication is that the deposits are made annually, while compounding are made quarterly.
So, we should construct an equivalent model, which will smoothly combine/treat these features.
7% annually compounded quarterly works as the effective quarterly rate r = 0.07/4;
then the effective annual growth coefficient is
t = = 1.071859031, or an effective annual rate q = 0.071859031.
Now this given saving plan as an equivalent to the ordinary annuity
with annual deposits of P5000 and with effective annual rate q = 0.071859031 compounding yearly.
Therefore, we can apply the standard formula for future value of such ordinary annuity
FV = = 69691.82.
ANSWER. The future value is P69691.82.
Solved completely, with complete explanations.
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We equivalently transformed the given saving plan into another saving plan,
where deposits are synchronized with compounding.