Simple Interest  Basics
Interest is the money charged for borrowing money or paid to somebody who
invest money
The rate of Interest is the payment made by the borrower expressed as
a percentage of capital
How do you calculate the interest and the future value (accumulated amount) for an
investment with a simple interest rate over a period of time?
Simple interest questions can be solved by applying the following formulae:
English version
Time expressed in years
FV = PV + I

I: interest after t years.
PV: principal (initial value of an investment or present value)
r: annual interest rate in percentage (%)
FV: accumulated amount (final value of an investment or
future
value)

Italian version
Time expressed in years
M = C + I

I: interest after t years
C principal or present value (capitale)
r: annual interest rate in percentage (%)
M: accumulated amount or future value (montante) 
Example 1:
Michelle invested € 5,000.00 in mutual fund with the interest rate of 4.8%.
How much interest would she earn after 2 years?
Answer :
PV = € 5,000.00
r = 4.8%
t = 2
I = (PV × r × t)/100
I = (€ 5,000.00 x 4.8 x 2)/100 = € 480.00
Hence, Michelle would earn € 480 after 2 years.
Example 2.
Jeff has one savings account with the interest rate of 3.3% in a bank. If he deposits
€1200.00
to the savings account how much money
will he have after 6 years?
Answer:
PV = €1200.00
r = 3.3%
t = 6
FV = [PV × (100 + rt)]/100
FV= [€1200.00 x (100 + 3.3 X 6)]/100= € 1437.60
Hence, Jeff will have
= € 1,437.60 after 6 years.
Solve the interest problem below:
1) The Amount you borrowed (principal) is € 166, Annual Interest Rate is 7%,
Time Period is 3 years.
Amount (future value) after 3 years is:_________ Interest after 3 years is:______
2) The Amount you borrowed (present value or principal) is €1139, Annual Interest Rate is
4%, Time Period is 19 years.
Amount (accumulated amount) after 19 years is :________
Interest after 19 years is:_____
3) The Amount you borrowed (present value) is € 657, Annual Interest Rate is
11%, Time Period is 6 years.
Future value after 6 years is:________
Interest after 6 years is:_____
Simple Interest  Period of time is a fraction of the year
The Simple Interest formula applies to shortterm investments (less
than a year). Typical Situation: You invest/lend/borrow money for less than a
year; at maturity you receive/repay the principal (face value or PV) plus
interest (PV x r x t)/100.
For Example
 If you invest € 100 in a checking account that returns 4% per year,
you’ll get €104 in a year.
 If you invest €100 in a current account that returns 4% per year; you’ll
get $102 in 6 months.
 If you invest $100 in a checking account that returns 4% per year, you’ll
get $101 in a quarter (3 months)
Time expressed in months
English
Italian
FV = PV + I
English
Italian 
I: interest after m
months.
PV: principal (initial value of an investment or present value)
r: annual interest rate in percentage (%)
FV: accumulated amount (final value of an investment or
future
value)

Time is expressed in days according to the calendar year
we
are referring to exact simple interest and the fraction of the year
is based on 365 days
English
Italian
FV = PV + I
English
Italian 
ANNO CIVILE
I: interest after d days.
PV: principal (initial value of an investment or present value)
r: annual interest rate in percentage (%)
FV: accumulated amount (final value of an investment or
future
value)

Time is expressed in days according to the commercial
year
we
are referring to ordinary simple interest and the fraction of the year
is based on 360 days
English
Italian
FV = PV + I
English
Italian 
ANNO COMMERCIALE
I: interest after d days.
PV: principal (initial value of an investment or present value)
r: annual interest rate in percentage (%)
FV: accumulated amount (final value of an investment or
future
value)

Calculating the Number of Days of a Loan
Steps for Determining the Number of Days of a Loan:
 Step 1. Determine the number of days remaining in the first month by
subtracting the loan date from the number of days in that month.
 Step 2. List the number of days for each succeeding whole month.
 Step 3. List the number of loan days in the last month.
 Step 4. Add the days from Steps 1, 2, and 3.
Determining the Maturity Date of a Loan
Steps for Determining the Maturity date of a Loan
 Step 1. Find the number of days remaining in the first month by
subtracting the loan date from the number of days in that month.
 Step 2. Subtract the days remaining in the first month (Step 1) from the
number of days the loan.
 Step 3. Continue subtracting the number of days in each succeeding whole
month, until you reach a month in which the difference is less than the
total days in that month. At that point, the maturity date will be the day
of that month that corresponds to the difference.
Inverse Formulae:

the unknown 
TIME 
Present Value 
rate of interest 
time 
years 



months 



days/365 



days/360 



Inverse Formula of PV from FV:

year 
months 
days/365 
days/360 
Present Value 




GLOSSARY
– Interest Problems
English

Italian

Notes

charge (v) 
addebitare 

borrow (v) from 
prendere
a prestito da 

borrower 
debitore
di un prestito 
mutuatario 
rate of interest 
tasso
di interesse 
i.g.
:5% per year 
mutual fund 
fondo
comune d'investimento 

savings account 
deposito
a risparmio 

checking account 
conto
corrente bancario 
also
"current account" 
maturity 
scadenza 

calendar year 
anno
civile 
365
days per year 
commercial year 
anno
commerciale 
360
days per year 
simple interest 
interesse
semplice 

compound interest 
interesse
composto 

accrued interest 
interessi
maturati 

present value 
valore
attuale 

future value 
montante 

lend (v) to 
dare
a prestito a 

lender 
creditore
di un prestito 
mutuante 
loan 
prestito 

loan date 
data
erogazione del prestito 
da
cui decorrono gli interessi 
unknown 
incognita 










