Question

Shelley wants to cash in her winning lottery ticket. She can either receive six, $193,000 semiannual payments starting today, or she can receive a single-amount payment today based on a 6% annual interest rate. What is the single-amount payment she can receive today?

Answer 1

$1,045,517.95

Step-by-step explanation:

Data provided in the question:

Semiannual payments = $193,000

Number of semiannual payments, n = 6

Annual interest rate, i = 6% = 0.06

when compounded semiannually = 6% ÷ 2 = 3% = 0.03

Now,

Single Payment = Semiannual payments × PVAF

here,

PVAF = [ 1 - (1 + i )⁻ⁿ ] ÷ i

or

PVAF = [ 1 - (1 + 0.03 )⁻⁶ ] ÷ 0.03

or

PVAF = 5.4172

Therefore,

Single Payment = $193,000 × 5.4172

= $1,045,517.95