Given,
Quarterly Payments= 5,000
Principle Amount = 65,000
Rate = 7% p.a
principle=payment
[nr1−(1+nr)−nt]65000=5000[40.071−(1+40.07)−4t]65000=5000[40.071−(1+0.0175)−4t]500065000=[0.1751−(1−0.0175)−4t]12×0.0175=[1−(1.0175)−4t]0.2275=1−0.0175−4t0.7725=1.0175−4t
Now taking log on both sides,
log(0.7725)=log(1.0175)−4tlog(0.7725)=−4tlog(1.0175)t=−4tlog(1.0175)log(0.7725)t=3.7196
Therefore, total number of payments if made quarterly will be:
number of payments
=3.7196×4=14.8784around 15 payments
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