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Overview

Formulas
Task 1
Task 2
Task 3
Task 4
Task 5
Task 6

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Sheet 1: Formulas

Annuity

Value of Annuity, given Present Value

Value of Annuity, given Future Value

Future Value of Annuity

Future Value of Annuity Due

Present Value of Annuity

Present Value of Annuity Due

Present Value of Perpetuity

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Sheet 2: Task 1

Task 1

Find the monthly annuity which you will receive through 15 years, by having 3000 PLN on your deposit, 5 years before getting the first payment.

Monthly interest rate at 15%.

Solution:

1. At first, find the future value of your deposit, after 5 years:

PV

3000

n

5

m

12

r

1,25%

monthly

equation:

6 321,54 zł

function:

6 321,54 zł

2. Compute single payment:

PVAn

6 321,54 zł

r

1,25%

monthly

n

15

m

12

equation:

88,48 zł

function:

88,48 zł

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Sheet 3: Task 2

Task 2

Find the amount of money, which you should pay for your deposit, to receive 5000 PLN of half-year annuity due after 5 years, through 20 years.

Bank uses half-yearly interest at 6%.

Solution:

1. At first, compute present value of annuity due:

PMT

5 000,00 zł

r

6%

half-yearly

n

20

m

2

equation:

79 745,37 zł

function:

79 745,37 zł

2. Then compute the present value of your deposit:

FV

79 745,37 zł

r

6%

half-yearly

n

5

m

2

equation:

44 529,40 zł

function:

44 529,40 zł

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Sheet 4: Task 3

Task 3

Your grandfather is going to pay 20 000 PLN for a bank deposit, with effective rate at 10%.

He would like to make it enough for a scholarship for you, in the amount of 500 PLN monthly (ordinary annuity) by five years of study.

Is it possible? If not, what advice can you give to grandfather?

Solution:

1. Find the nominal interest rate, equivalent to the effective one:

ref

10%

r nom

#ADDIN?

annually

PV

20000

2. Then check, how many scholarships can you get:

PMT

500

PVAn

20000

r

9,57%

annually

n

4

m

12

equation:

PMT

6 250,79 zł

Use "Goal seek"

function:

PMT

500

n

#NUM!

Answer:

3. In that case, how much should your grandfather pay at the beginning on this deposit?

PMT

r

annually

n

m

equation:

function:

4. Or maybe bank should offer better effective rate?

PVAn

PMT

r

annually

n

m

equation:

ref

Use "Goal seek"

function:

r

ref

5. What about reducing the amount of scholarship?

PVAn

r

annually

n

m

equation:

PMT

function:

PMT

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Sheet 5: Task 4

Task

A brand new television costs 800 PLN. We can buy it in installments by paying for 2 years at the end of each quarter, 140 zł.

The second eventuality is to take a bank loan in the amount of 800 PLN, which will bear interest of 7% per quarter and will be repaid in equal quarterly installments over two years.

Which option is more profitable?

Solution:

loan

installments

PV

800

FV

0

n

2

m

4

quarterly r

7%

8,15%

loan

is/are more profitable

PMT

133,97 zł

installments

is/are more profitable

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Sheet 6: Task 5

Task

The client of the bank wants to change quarterly ordinary annuity to monthly one. Bank offers interest rate at 12% quarterly and quartlerly payment in the amount of 1500 PLN.

Find the monthly annuity.

Solution:

1. At first, find the nominal, monthly interest rate:

Nominal, annual interest rate:

48,00%

for quarterly deposit

Effective interest rate:

#ADDIN?

Nominal, annual interest rate:

#ADDIN?

for monthly deposit

monthly:

#ADDIN?

2. Then, compute the present value of annuity for quarterly payments...:

PMT

1500

r

48,00%

annually

n

1/4

m

4

equation:

PVAn

1 339,29 zł

function:

PVAn

1 339,29 zł

3. … to finally find the single payment of new, monthly annuity:

PVAn

r

monthly

n

m

equation:

PMT

function:

PMT

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Sheet 7: Task 6

Task

The Bank intends to provide to the University an annual payment of 50 000 zł for the purpose of development of scientific research.

What amount must be paid to the bank by sponsor, to ensure uninterrupted payments to the university? Bank offers deposit at 10% annually.

Solution:

PMT

50000

r

10%

PVP

500 000,00 zł