TIME VALUE OF MONEY: ANNUITY CASH FLOWS
Would you rather have a savings account that paid interest compounded on a monthly basis, or one that compounded interest on an annual basis? Why?
Compound interest arises when interest is added to the principal. Therefore, the interest that has been added also earns interest. This addition of interest to the principal is called compounding. If the savings account has $1,000 initial principal and 20% interest per year, the account will have a balance of $1200 at the end of the first year, $1440 at the end of the second year. Frequent or monthly compounding increases the future value (Cornett, Adair, & Nofsinger, 2014, page 109-110).
What is an amortization schedule and what are some of its uses?
It is the schedule of payments for paying off a loan. An amortization schedule breaks down the payments into interest and principal, which is helpful because with an amortized loan amounts ...view middle of the document...
Thus, the tax deductible part, which is the interest payment, is larger in the beginning years (Cornett, Adair, & Nofsinger, 2014, page 114-116).
What is the difference between an ordinary annuity and an annuity due?
Annuities can be divided into two types based on the exact time when the payments occur in a given period. The payments could either occur at the beginning of every period or the payments could occur at the end of every period. For instance, if one takes a house on rent, the rent is usually paid in advance whereas a mortgage payment is usually made at the end of every period. This means that the payments that are made at the end of every period are called ordinary annuity. This is because ordinary annuity is the usual state of affairs. Under normal circumstances all annuities are paid at the end of the period.
Therefore, when annuity payments are made in advance, like in house rents, they are called annuity due. The difference in the formula to calculate the two different types of annuities is very small (Cornett, Adair, & Nofsinger, 2014, page 108).
What is the future value of a $ 500 annuity payment over five years if interest rates are 9 percent? Recalculate the future value at 8 percent interest, and again at 10 percent interest.
FVA5 = $500 x (1+0.09)5 -1 = $500 x 5.9847 = $2,992.36
FVA5 = $500 x (1 + 0.08)5 -1 = $500 x 5.8666 = $2,933.30
FVA5 = $500 x (1 + 0.10)5 – 1 = $500 x 6.1051 =$3,052.55
What is the present value of a $700 annuity payment over four years if interest rates are 10 percent? Recalculate the present value at 9 percent interest, and again at 11 percent interest.
PVA4 = $700 x 1 – __1____
(1 + 0.10)4 = $700 x 3.1698655 = $2,218.91
PVA4 = $700 x 1 – __1__
(1+0.09)4 = $700 x 2.8528789 = $1,997.01
PVA4 = $700 x 1 - ___1__
(1+0.11)4 = $700 x 3.48685205 = $2,440.79