someone please help, I’m having trouble distinguishing when to 1 + r*(t/360) or 1 + r^(t/365). for the below two questions, i did the discounting completely the opposite way. could someone please clarify how to distinguish which format to use for discounting??? - bolded below

Q1

A stock is currently priced at $110 and will pay a $2 dividend in 85 days and is expected to pay a $2.20 dividend in 176 days. The no arbitrage price of a six-month (182-day) forward contract when the effective annual interest rate is 8% is closest to:

$110.20.

$110.00.

$110.06.

Explanation

In the formulation below, the present value of the dividends is subtracted from the spot price, and then the future value of this amount at the expiration date is calculated.

(110 – 2/**1.08^85/365** – 2.20/**1.08^176/365**) **1.08^182/365** = $110.06

Alternatively, the future value of the dividends could be subtracted from the future value of the stock price based on the risk-free rate over the contract term.

(Study Session 14, Module 37.4, LOS 37.a)

Q2

Cal Smart wrote a 90-day receiver swaption on a 1-year LIBOR-based semiannual-pay $10 million swap with an exercise rate of 3.8%. At expiration, the market rate and LIBOR yield curve are:

Fixed rate 3.763%

180-days 3.6%

360-days 3.8%

The payoff to the writer of the receiver swaption at expiration is closest to:

$3,600.

$0.

-$3,600.

Explanation

At expiration, the fixed rate is 3.763% which is below the exercise rate of 3.8%. The purchaser of the receiver swaption will exercise the option which allows them to receive a fixed rate of 3.8% from the writer of the option and pay the current rate of 3.763%.

The equivalent of two payments of (0.038 - 0.03763) × (180/360) × (10,000,000) will be made to the receiver swaption. One payment would have been received in 6 months and will be discounted back to the present at the 6-month rate. One payment would have been received in 12 months and will be discounted back to the present at the 12-month rate

The first payment, discounted to the present is (0.038 - 0.03763) × (180/360) × (10,000,000) × ( **1/1.018**) = $1,817.28.

The second payment, discounted to the present is (0.038 - 0.03763) × (180/360) × (10,000,000) × ( 1/1.038) = $1,782.27

The total payoff for the writer is -$3,599.55.

(Study Session 14, Module 38.6, LOS 38.j)