Question

• Find the present worth of a series of equal quarterly payments of ₱ 750.00 for 16 years with the first payment starting three months from now. The applied interest rates are: 2% compounded quarterly for the first five years, 5% compounded quarterly for the next four years, and 2% compounded quarterly for the remaining seven years.

Answer 1

PVIFA = Present Value Interest Factor Annuity

(Assuming that the given rates of 2%,5% are rates for quarter and not annual)

PVIFA(2%,20quarters) = 16.35143

PVIFA(5%,36quarters) = 16.54685

PVIFA(5%,20quarters) = 12.46221

PVIFA(2%,64quarters) = 35.921415

PVIFA (2%,36quarters) = 25.48884

Quarterly Payment amount = 750

Present Worth

= 750 x [16.35143 + (16.54685-12.46221) + (35.921415-25.4884)]

= 23,152 (rounded off to nearest whole number)

Note :

5 years = 20 quarters

9 years = 36 quarters

16 years = 64 quarters

The PVIFA is calculated using calculator. The same can also be calculated using a formula

= Sum [1/(1+r)^n]

For example,

for PVIFA(2%,20quarters)

= Sum[1/(1.02)^n] (n is changed from 1 to 20 and all are added)