Determining the Worth of a Policy

Part 1
Question 1
Answer
The policy is not worth it.
The table below summarizes the policy cash inflows and outflows
Time Cash flow
1 $ 500.00
2 $ 600.00
3 $ 700.00
4 $ 800.00
5 $ 900.00
6 $ 1,100.00
65 $ (275,000.00)
Interest rate of 11% is applicable for time 1 to 6 and 7% is applicable for time 7 to 65
To determine if the policy worth buying or not, the Net Present Value of the cash flows should
be greater than zero.
The Net present value is calculated using the formula below:
NPV= Present value of cash inflows plus present value out outflows
NPV= ∑
i=1
6
CF t∗(1+11 %)−t + CF65*(1+7%)-65
The table below summarizes the present values of cash flows

Time Cash flow Present Value
1 $ 500.00 $450.45
2 $ 600.00 $486.97
3 $ 700.00 $511.83
4 $ 800.00 $526.98
5 $ 900.00 $534.11
6 $ 1,100.00 $588.10
65 $ (275,000.00) $(3,383.66)
Total $(285.21)
The Net present Value is -$285.21. Since this is less than zero, the policy is not worth it.

Question 2
Answer
A lump sum of $13,335.22 should be invested in B today.
To find the lump sum, we need to solve the equation:
Future Value of Investment B = Future Value of Investment A
Investment A
n =15-year annuity
PMT= $1,500
i(12) =interest rate of 8.7 percent compounded monthly
Investment B
n =15-year Lump sum
i(52) = interest 8 percent compounded weekly
Step 1: Find annual effective rate of interest, i for both investments
1+i = (1+ j
n )n (Madura, 2009)
Where i is the effective rate and j is the nominal rate of interest
Investment A
i = (1+i(12)/12)12 -1
=(1+0.087/12)^12-1

=9.0554%
Investment B
i = (1+i(52)/52)52 -1
=(1+0.08/52)^52-1
=8.3220%
Step 2: Find Future Value of Investment A
Future Value of Annuity = PMT * [ (1+ i)15−1 ¿¿¿ i ]
= 1500 * [ (1+9.0554 %)15−1
9.0554 % ]
= $44,233.69
Step 3: Solve the equation: Future Value of Investment B = Future Value of Investment A
Future Value of Investment B= Future Value of Investment A
Lump sum*(1+8.3220%)15 =$44,233.69
Lump sum =44233.69/(1+8.3220%)15
Lump sum = $13,335.22