QR Workshop – FinanceNovember 5, 2015ANDREAS KAKOLYRIS-YOONHEE KANGQUANTITATIVE REASONING FELLOW, NYCCT

Learning Objectives

1) Simple Interest 2) Compound Interest Rate3) Annuity

Simple Interest• Simple interest is a one-time percent of an amount of money.• With simple interest, you pay/earn the same amount of

interest every year.

You invest $1,000 at 20 % simple interest!• Interest = 1000(0.2)=200• Value in one year = 1,000 (initial invest) + 200 (interest)= $1200• Value in two years = 1,000+ 400 (interest for 2 years) = $1,400

$1,000 1,200 1400 1,600

Today 1 2 3 4

1,800 …

Simple Interest

I = PrtFuture Value (FV) = P + I = P(1+rt)

• I = interest• P = the beginning amount borrowed or invested ("Principal")• r = interest rate • t = time; the length of the time loaned or invested• FV (A)= the final amount repaid or accumulated

Compound Interest

• Compound interest is a percent of an original amount, as well as a percentage of the new amount including previously calculated interest.

• With compounding we work out the interest for the first period, add it the total, and then calculate the interest for the next period.

interest on interest!

Compound Interest Rate

You invest $1,000 at 20% !!!(interest is compounded annually)

• Interest 1000(0.2)=200• Value in one year=principal +interest =1000 + 200 =1000(1.2) =

$1200• Value in two years= 1200(1.2)== $1440

…..$1,000 1,200 1,440 1,728

Today 1 2 3 4

2,073.6

Compound Interest Rate

FV = PV(1 + r)t

Compound Interest Rate

FV = PV• r = quoted rate• n = the number of times that interest is compounded per year• t = the number of years the money is invested or borrowed for

**Interest can be compounded annually (once a year) n=1semiannually (twice a year) n=2quaterly (4 times a year) n=4

monthly (12 times a year) daily (365 times a year)

Simple VS Compound

Year20% Simple Interest 20% of Compound Interest

Principal Interest Principal Interest0 (Today) 1000 1000

1 1000 200 1200 2002 1000 200 1440 2403 1000 200 1728 2884 1000 200 2073.6 345.6

Value after 4 yr

1800 2073.6

Compound Interest RateFV = PV

You’ve probably seen the phrase “annual percentage rate” or “APR” on your monthly credit card statement ! What is APR?

APR is an annual interest rate with monthly or daily compounding• An APR=18% with monthly payments is

really 1.5% per month (r/n=0.18/12=0.015)

Compound Interest Rate

FV = PV

An annual interest rate with monthly or daily compounding

Compound Interest Rate_Example1Find the FV of $800 after 5 years with APR=12%

with monthly compounding

Today 1 2 3 4 5

FV800

Compounding

Compound Interest RateFV = PV

Today 1 2 3 4

FVPV

Today 1 2 3 4

FV

PV

Compounding

Discounting

we moved single cash flows forward and backward in time.