A customer, age 45, invests $100,000 in a variable annuity contract. It imposes an 8% charge if the contract is surrendered within the 1st 8 years; and a 4% charge if the contract is surrendered in years 9 and 10. Thereafter, there is no surrender charge. The contract has a Guaranteed Minimum Income Benefit (GMIB) that promises to annuitize the account at a value of $180,000 starting at age 60. After holding the contract for 5 years, the separate account has a net asset value of $120,000. The insurance company makes an offer to the client to buy back the contract at $121,000 with no surrender charges imposed. Assuming that the client's investment objectives have not changed, the best advice to the client is to:.

the client should wait 10 more years until the contract is worth $180,000 since he will earn a slightly higher interest rate

Explanation:

we must determine the effective interest earned by the client if he accepts the company's proposal:

future value = present value x (1 + r)ⁿ

121,000 = 100,000 x (1 + r)⁵

(1 + r)⁵ = 121,000 / 100,000 = 1.21

⁵√(1 + r)⁵ = ⁵√1.21

1 + r = 1.0389

r = 0.0389 = 3.89%

if the client waits 10 more years until he is able to annuitize the account, he should earn:

180,000 = 100,000 x (1 + r)¹⁵

(1 + r)¹⁵ = 180,000 / 100,000 = 1.80

¹⁵√(1 + r)¹⁵ = ¹⁵√1.80

1 + r = 1.03996

r = 0.03996 = 4%

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