Question

Could you please help me with these 3 questions?
An insurance company is offering a new policy to its customers. Typically the policy is bought by a parent or grandparent for a child at the child's birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company: First birthday Second birthday Third birthday Fourth birthday Fifth birthday Sixth birthday Ꮎ Ꮎ Ꮎ Ꮎ Ꮎ Ꮎ 900 900 $ 1,000 850 $ 1,100 950 After the child's sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $400,000. If relevant interest rate is 12 percent for the first six years and 7 percent subsequent years, what would the value of the deposits be when the policy matures? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value

Answer 1

Answer :

(1)

We need to find the FV of the premiums to compare with the cash payment promised at age 65. We have to find the value of the premiums at Year 6 first since the interest rate changes at that time. So:

FV1 = $900(1.12)^5 = $1,586.1075

FV2 = $900(1.12)^4 = $1,416.1674

FV3 = $1,000(1.12)^3 = $1,404.928

FV4 = $850(1.12)^2 = $1,066.24

FV5 = $1,100(1.12)^1 = $1,232

Value at Year 6 = $1,586.1075 + $1,416.1674 + $1,404.928 + $1,066.24 + $1,232 + $950

= $7,655.4429

Future Value = $7,655.4429 x (1.07)^59 = $414,584.64

So, Future Value = $414,584.64

(2)

Discount rate for six month period = [1 + ( 0.10 / 360 )]^180 - 1 = 5.13%

Present value of 40 payments of $1,200,000 :

PV = A/r*[1-(1+r)^(-n)]

=1200000/0.0513*[1-(1+0.0513)^(-40)]

= $20,229,554.83

Total Present Value = 2,400,000 + 20,229,554.83*(1+0.0513)^(-1) = $21,642,418.75

So, Present Value = $21,642,418.75

(3)

Annual Payment = $7,700

Present Value = $121,681

Interest Rate = 5%

Present Value of Annuity :

p[1-(1+r)**]

= 7,700 x [1 - (1+0.05)^-n)] / 0.05

By filling 32 in place of n

= 7,700 x [1 - (1+0.05)^-32)] / 0.05

= 7,700 x 15.8026766684

= 121,680.61

So, Correct Option is :

32.00 Years