Question

What is the relationship between the value of an annuity and the level of interest rates? Suppose you just bought a 10-year annuity of$5,200 per year at the current interest rate of 10 percent per year. What happens to the value of your investment if interest rates suddenly drop to 5 percent? What if interest rates suddenly rise to 15%? Please use excel to calculate.

Answer 1

		10%		5%		15%
Year	Cash Flow	Discounting Factor [1/{1.1^year}]	FV of Cash Flows [Cash Flow*Discounting Factor]	Discounting Factor [1*(1.05^year)]	FV of Cash Flows [Cash Flow*Discounting Factor]	Discounting Factor [1*(1.15^year)]	FV of Cash Flows [Cash Flow*Discounting Factor]
1	5200	1.1	5720	1.05	5460	1.15	5980
2	5200	1.21	6292	1.1025	5733	1.3225	6877
3	5200	1.331	6921.2	1.157625	6019.65	1.520875	7908.55
4	5200	1.4641	7613.32	1.21550625	6320.6325	1.74900625	9094.8325
5	5200	1.61051	8374.652	1.276281563	6636.664125	2.011357188	10459.05738
6	5200	1.771561	9212.1172	1.340095641	6968.497331	2.313060766	12027.91598
7	5200	1.9487171	10133.32892	1.407100423	7316.922198	2.66001988	13832.10338
8	5200	2.14358881	11146.66181	1.477455444	7682.768308	3.059022863	15906.91889
9	5200	2.357947691	12261.32799	1.551328216	8066.906723	3.517876292	18292.95672
10	5200	2.59374246	13487.46079	1.628894627	8470.252059	4.045557736	21036.90023
		Sum of PVs =	91162.06872	Sum of PVs =	68675.29324	Sum of PVs =	121416.2351

From above, it can be interpreted that, as the interest rate decreases, the price of annuity also decreases & as the interest rate increases, the price of annuity also increases. So, we can say that, there is Direct relationship between the interest rate and value of annuity.

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