Question

If Php 10,000 is deposited each year for 9 years, how much annuity can a person get annually from the bank every year for 8 years starting 1 year after the 9th deposit is made? Cost of money is 14%

Answer 1

Compute future value of deposited annuity as under:

FV = P x [{(1 +r)n -1}/r]
Where,
FV = Future amount
P = Periodic payment
n = no. of periods
r = Rate of interest = 14% = 0.14

FV = 10,000 x [{(1 +0.14)9 -1}/0.14]
      = 10,000 x [{(1.14) 9 -1}/0.14]
      = 10,000 x [(3.2519485 -1)/0.14]
     = 10,000 x (2.2519485/0.14)
     = 10,000 x 16.085347
     = 160853.47

This maturity amount 160853.47 is the present value to get 8 annual future cash flows which can be computed using formula for PV of annuity as under:

PV = P [{1-(1+r)-n}/r]
Where,
PV = Present value before getting the annuity  
P = Periodic cash flow
n = No. of periods = 8
r = Rate of interest = 14% = 0.14
Putting all these values we get the required cash flow amount as:
160853.47 = P * [{1 – (1 + 0.14)^-8} / 0.14]
160853.47 = P * [{1 – (1.14)^-8} / 0.14]
160853.47 = P * [(1 – 0.350559) / 0.14]
160853.47 = P * [0.649440 / 0.14]
160853.47 = P * 4.638863
P = 160853.47 / 4.638863
P = 34675.19