Interest Problems
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Warm-Up  Interest Simple Discount Interest exercises Interest & Discount Format versione pdf

 

 

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 short-term 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