This document provides examples of calculating various types of annuities and rates of return. It shows how to determine: 1) The number of annuity payments needed to reach a target accumulation amount given an interest rate. 2) The number of years needed for an investment to double or reach a desired return amount given an interest rate. 3) The implied annual rate of return given a monthly annuity payment, future value, and number of periods. 4) The compound annual growth rate given earnings amounts over several years. 5) The present value of annuities that start later than the first period. 6) How to combine the present value of an annuity with a lump sum payment.

1. Complex
Applications

2. Number of Annuities needed for target
accumulation
• Compute the example given in the page than
solve following sums.
1. How many Annuities of Rs. 300 each are
required to achieve an accumulation of Rs.
3450 at an interest rate of 10%?
Answer:- N = 8.03 (approx 8 annuities)
2. How many Annuities of Rs. 150 each are
required to achieve an accumulation of Rs.
1450 at an interest rate of 8%?
Answer:- N = 7.09 (approx 7 annuities)

3. Number of years needed for Growth in
Investment
• Previous one was to find out the annuities,
here we will compute the number of years
to doubling or to reach to the level to the
desired level of return.
1. How many years it shall take for Rs. 450
to grow to Rs. 4500 at an interest rate of
12%?
Answer:- N = 6.957

4. Rate of Return on an Annuity
• Compute rate of return on a monthly annuity
of Rs. 3000 that Provides Rs. 45000 after 5
years.
Answer:- I/y = 6.5524%
here, N = 5*12 = 60
(Note=
Here we are calculating interest rate and FV
{future value} is given so PMT will not be
remain Negative.)

5. Rate of Growth
• The earning of Mr. Y during was 1500,
4500, 6500, 7800, 7900. compute the
Growth in earnings (CARG).
• ( CARG = Compound Annual Rate
Growth)
• Answer :- I/y = 51.4899%
• ( Note =
here Present Value will be taken
negative.)

6. Ordinary Annuity beginning Later than
1st Year
• What is the present value of a 7 year annuity
of Rs. 250 starting at the end of 4 years from
now considering a discount rate of 12%.
• Answer =
we have to calculate this sum into two parts

7. • Part 1 :-
• Find PV of the 7 years annuity at the end
of 3rd year.
Answer:- PV2 = Rs. 1500
• Part 2 :-
• Find PV of Pv2
Here, N = 4
Answer = Rs. 193.939

8. Annuity due beginning later than 1st
year
• What Is the present value of a 4 year annuity of Rs. 1500
starting at the beginning of year 4 from now considering
a discount rate of 10%.
• Part 1:-
• Find PV of the 4 years annuity at the end of beginning of
4th year ( calci must be in beginning mode )
Answer = PV4 Rs. 5,330.271
• Part 2 :-
• N = 3, FV = ,330.271 (calci must be in END mode)
Answer:- PV = 274.433

9. Combining annuity and Lump sum
• A bond with par of Rs. 1200 shall pay a
coupon of 7% and pay back Rs. 1200 at
maturity which is 4 years from today. If
discount rate is 12%, find PV.
• Solution:-
PMT(coupon) = 100 * 7% = 7
Answer: - PV = - 783.883

10. Thank you