Question

Assuming a 12% annual interest rate, determine the present value of a five-period annual annuity of $5,000 under each of the following situations:
1. The first payment is received at the end of the first year, and interest is compounded annually.
2. The first payment is received at the beginning of the first year, and interest is compounded annually.
3. The first payment is received at the end of the first year, and interest is compounded quarterly.
Depoosite date: 12/31/17, i=?, n=?, Deposit= $4100, PV - 12/31/16: ?
Deposite date 12/31/18, i=?, n=?, Deposit=$4100, PV -12/31/16: ?
Deposite date: 12/31/19, i=?, n=?, Deposit= $4100, PV- 12/31/16: ?
Deposti date: 12/31/20, i=?, n=?, Depostie= $4100, PV - 12/31/16: ?
Deposit date: 12/31/21, i=?, n=?, deposite=$ 4100, PV - 12/31/16: ?

Answer 1

Solution :

Annual payment = $\ 5000$

1. The rate of interest annually = 12%

Present value $=\ 5000 \times \text{PVA of} \ \ 1(12\%, 5)$

                      $=\ 5000 \times 3.60478$

                     = $ 18,023.90

2. The rate of interest annually = 12%

Present value $=\ 5000 \times \text{PVAD of} \ \ 1(12\%, 5)$

                      $=\ 5000 \times 4.03735$

                     = $ 20,186.75

3. The rate of interest annually = 12%

The rate of interest quarterly = 3%

Present value = $\ 5000 \times \text{PV of} \ \ 1(3\%, 4) + \ 5000 \times \text{PV of} \ \ 1(3\%, 8) +\ 5000 \times \text{PV of} \ \ 1(3\%, 12)$ $+\ 5000 \times \text{PV of} \ \ 1(3\%, 16) + \ 5000 \times \text{PV of} \ \ 1(3\%, 16)$

$= \ 5000 \times 0.88849 + \ 5000 \times 0.78941 + \ 5000 \times 0.70138 + \ 5000 \times 0.62317 + \ 5000 \times 0.55368$$=\ 17,780.65$