Module 1

Question 1

Future Value of a Lump Sum (FV)

Answer 1

FV: Future value
PV: Present value
i: Interest rate
N: Number of years

[10 I/YR, 3 N, -100 PV, FV] = 133.1

FV = PV ( 1 + i ) ^N

Question 2

Present Value of a Lump Sum (PV)

Answer 2

FV = 133.1
I = 10%
N = 3 years
What is PV?

[133.1 FV, 10 I/YR, 3 N, PV] = -100.0

PV = ( ^FV/_{((1 + i)^N)}) = FV ( ¹/_{((1 + i)^N)})

Question 3

Future Value of an Annuity (FVA)

Answer 3

FVA: Future value of an annuity
PMT: The payment at the end of every period, which is a constant.
i: Interest rate
N: Number of years

[-100 PMT, 10 I/YR, 3 N, FV] = 331.0

Question 4

Present Value of an Annuity (PVA)

Answer 4

PMT = 100
i = 10%
N = 3 years
What is the PVA?

[100 PMT, 10 I/YR, 3 N, PV] = -248.69

Question 5

Other Compounding Periods

Answer 5

FV = PV ( 1 + (ⁱ/_M)) ^NM

M: Number of compounding periods within a year
Semi-annual compounding, M=2
Quarterly compounding, M=4
Monthly compounding, M=12
Daily compounding, M=360

Here you need to divide the interest rate by the number of compounding periods in a year (M) and multiply N by M.

Question 6

If you deposit 100 today into your bank account, what would the account balance be in 3 years if the interest rate is 10% compounded monthly?

Answer 6

[-100 PV, 10/12 I/YR, 3X12 N, FV] = 134.82

Question 7

You borrow a home mortgage loan of $100,000 today. The term is 15 years and the interest rate is 5%. What is the monthly payment? Note that home mortgages are typically monthly payment.

Answer 7

[100,000 PV, 5/12 I/YR, 15X12 N, PMT] = -790.79

Question 8

You borrow $100,000 as a mortgage loan today. The loan requires a monthly payment of $790.79 for 15 years. What is the interest rate for the loan?

Answer 8

In this example, you need to enter the payment as a negative number and the loan amount as a positive number, otherwise you will not get the right answer. When there are both cash inflow(s) and outflow(s) in the question, you need to tell the calculator which is inflow and which is outflow, otherwise the calculator will be utterly confused and quit. For example, in this question, the loan amount is your receipt, so it is an inflow, and you will need to make the payment, so it is an outflow.

[100,000 PV, -790.79 PMT, 15X12 N, I/YR] = .4167%

In this example, it is monthly payment and monthly compounding, so the solution you get from the calculator, .4167%, is a monthly figure. But interest rate is normally stated as an annual rate, so multiply this number by 12 to get the annual rate of 5%.

.4167% (12) = 5%

Question 9

Present Value of a Perpetuity

Answer 9

PV (Perpetuity) = ^PMT/_i

Question 10

An interest rate is normally stated as an rate and includes the number of per year.

Answer 10

1. annual
2. compounding periods

For example, the current 30-year mortgage rate is 4.5% (March 2014) with monthly compounding. The 4.5% is an annual rate. It is also called a nominal rate, or a quoted rate.

EAR (or EFF) - effective annual rate

Question 11

Effective annual rate formula

Answer 11

EAR = 1 + (ⁱ/_M)^M - 1.0

It means that i% compounded M times per year is effectively the same as EAR% compounded annually.