Question

Assume that the interest rate is 4% compounded monthly. Roy buys 100 shares of Moogle company, at the market price of $30 per share. For this he borrows the money from the bank. Assume that after six months he sells the shares for a price of $S per share. Find the minimal S for which Roy has enough money to fully pay back his loan to the bank. (Round to the nearest cents)

Answer 1

$30.61

Step-by-step explanation:

Data provided in the question:

Annual Interest rate = 4% = 0.04

Since compounded monthly

Therefore,

Monthly interest rate, r = 0.04 ÷ 12 = 0.0033

Price per share = $30

Number of shares purchased = 100

Total value of shares purchased = $30 × 100

= $3,000

Therefore,

the amount borrowed = Total value of shares purchased

= $3,000

Amount to be paid after 6 months = Principle × ( 1 + r )ⁿ

= $3,000 × ( 1 + 0.0033 )⁶

= $3,060.50

Therefore,

The minimal value of S

= Amount to be paid after 6 months ÷ Number of shares

= $3,060.50 ÷ 100

= $30.605 ≈ $30.61