Question

A contract can be fulfilled by making an immediate payment of $11,400 or equal payments at the end of every six months for 6 years. what is the size of the semi-annually payments at 11.8% compounded semi-annually?

A) $1,000
B) $1,200
C) $1,400
D) $1,600

Answer 1

The size of the semi-annually payments is $1,160.

Step-by-step explanation:

To find the size of the semi-annually payments, we can use the formula for the present value of an annuity:

`PV = C * (1 - (1 + r)^(^-^n^)) / r`

Where:
PV = Present value of the annuity
C = Size of the semi-annually payment
r = Interest rate per period
n = Number of periods

Plugging in the given values:

PV = $11,400
r = 11.8% / 2 = 0.059
n = 6 years * 2 = 12 periods

Solving for C, we get:

`C = PV * (r / (1 - (1 + r)^(^-^n^)))`

= $1,160

Therefore, the size of the semi-annually payments is $1,160.