Time Value of Money

Question 1

Simple Interest

Answer 1

1+it

Question 2

Real Rate of Interest Formula

Answer 2

(i - r) / (1 + r)

Question 3

Force of Interest for Simple Interest

Answer 3

i / (1 + it)

Question 4

Force of Interest for Compound Interest

Answer 4

ln( 1 + i)

Question 5

Net Present Value

Answer 5

total value of all cashflows either in or out divided by a discount rate, so basically present value for many different payments.

Question 6

Compound Interest

Answer 6

(1 + i) ^ t

Question 7

a(t)

Answer 7

accumulation function -> how much an investment of 1 dollar would grow to in a certain amount of time

Question 8

A(t)

Answer 8

a(t) * A(0) FYI: (A(0) is the principal)

Question 9

Present and Future Value

Answer 9

Using current interest rates, the value that the current money would grow to.

Question 10

Convertible monthly.

Answer 10

i^(12)

Question 11

i^(m)

Answer 11

( 1 + (i/m) ) ^ m

Question 12

Equivalent Rates of Interest and Discount

Answer 12

i = d / (1 - d)
d = i / (1 + i)

Question 13

Rate of Discount.

Answer 13

It is used to determine the current value by reducing future value. i.e. RoD = 0.07 and Money at time 1 is 100

Then money at time 0 is 93. Or if we had time 0, then time 1 is 93 * ( 1 / 0.93)

Question 14

Equation of Value

Answer 14

Equates the present value of all payments disbursed and received.

Question 15

Effective Annual Rate of Interest

Answer 15

( A(t) - A(t - 1) ) / A(t - 1)

Question 16

Effective Annual Rate of Discount

Answer 16

( A(t) - A(t - 1) ) / A(t)

Question 17

Force of Interest - 2 Formulas

Answer 17

1. Derivative of a(t) over a(t)

2. exp(integral with respect to t of the equation)