Birdie fry saves 500 at the end of every quarter in an ordinary annuity earning 7.2% interest compounded quarterly what is the amount of his savings and twenty years and interest will he have earned
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In 20 years there are 80 quarters. I'm assuming that 7.2% is the quarterly interest rate not the rate per annum. See later for alternative solutions.

1st quarter: 500+7.2%=500+500*0.072=500*1.072=536, assuming that each saving of 500 is subject to full interest in the same quarter (see later).

2nd quarter: 536+500+7.2% of (536+500)=1036*1.072=1110.59 approx.

3rd quarter: (1036*1.072+500)(1.072)=1726.55 approx, and so on.

There's a pattern:

(500*1.072+500*1.072^2+500*1.072^3+...+500*1.072^80).

That is, 500*1.072(1+1.072+1.072^2+...+1.072^79)=536(1.072^80-1)/(1.072-1)=536*3602.29=1,930,829 approx.

Depending on whether the first and each subsequent quarter is credited with full quarterly interest in the same quarter, the answer could be either 1,930,829 or 1,801,147 approximately, the lower amount being when interest is credited in the quarter following the savings deposit.

To find the interest we need to know how much was saved without interest=500*80=40,000.

Therefore the interest is 1,890,829 or 1,761,147.

If 7.2% is the annual rate, the quarterly rate is 1.8%. The adjusted figures require us to use the factor 1.018 instead of 1.072.

The total savings=89,555.38 or 87,971.89 and the corresponding interest is 49,555.38 or 47,971.89. (The first quarter's savings would be 509 instead of 536. The 2nd quarter's savings=1,027.16 approx, and so on.)

by Top Rated User (1.2m points)

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