Annuity is equal instalments for payments or receipts for specific period of time.
Or
Annuity is a series of equal payments or receipts occurring over a specific period of time.
Ist of annuity:
· Ordinary annuity:
In which instalments paid or receive at the end of the each period.
0 1st year 2nd year 3rd year 4rd year 5th year
100 100 100 100 100
We can find
Future value annuity = P[(1+r)n-1/r]
Present value annuity = P[1-(1+r)-n/r]
Q # 3(Ordinary annuity)
Joe Hernandez has inherited $ 25000 and wishes to purchase an annuity that will provide him with a steady income over the next 12 years. He has heard that the local saving and loan association is currently paying 6 percent compounded interest on an annual basis. If he were to deposit his funds, what year -end equal dollar amount ( to the nearest dollar ) would he able to withdraw annually such that he would have a zero valance after his last withdrawal 12 years from now?
Solution:
Rate of interest = 6 % p.a
No of year = 12
P.V = $ 25000
Installments (p) = ?
We know the formula of P.V annuity
P.V = P[ 1-(1+r)-n/r]
25000 = P[1-(1+0.06)-12/0.06]
P = 2982 will withdraw annuity
Q # 4 ( Ordinary annuity)
You need to have $ 50000 at the end of 10 year. To accumulate this sum, you have decided to save a certain amount at the end of each year of next 10 years and deposit it in the bank. The bank pay 8 % interest compounded annually for long-term deposits. How much will you have to save each year (to the nearest dollar)?
P = 2982 will withdraw annuity
Q # 4 ( Ordinary annuity)
You need to have $ 50000 at the end of 10 year. To accumulate this sum, you have decided to save a certain amount at the end of each year of next 10 years and deposit it in the bank. The bank pay 8 % interest compounded annually for long-term deposits. How much will you have to save each year (to the nearest dollar)?
Solution:
F.V = $ 50000
n = 10 year
r = 8 % p.a
Installments (p) = ?
By using F.V annuity formula
F. V a = P[(1+r)n-1/r]
50000 = P[(1+0.08)10-1/0.08]
P = 3453.04
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