The relationship between the value of an annuity and the level of interest rates
ID: 2631218 • Letter: T
Question
The relationship between the value of an annuity and the level of interest rates is as follows: The present value of an annuity rises as r drops; the future value of an annuity falls as r drops. Suppose you just bought a 8-year annuity of $3,000 per year at the current interest rate of 9 percent per year. The present value of this investment is $________. If interest rates suddenly drop to 4 percent, the present value of your investment increases to $_______. If, instead, interest rates suddenly rise to 14 percent, the present value of your investment decreases to $________.
Explanation / Answer
a)
PV = 3000 * [1-1.09^-8]/0.09 = 16604.46
b)
PV = 3000 * [1-1.04^-8]/0.04 = 20198.24
c)
PV = 3000 * [1-1.14^-8]/0.14 = 13916.59