Question

Maths of finance

**This task assesses the following learning
outcomes:**

- Time value for money and the rate of return
- Assess the simple interest and compound interest
- Net Present value in Capital Budgeting (Internal rate of return, Payback period)
- Annuities (PV, FV, Growth Annuities, types of Annuities)
- Perpetuities (PV, Growth Perpetuities)

2. The bank offers you some options, however, you can't withdraw it for 5 years:

a. 8% simple interest

b. 6% compounded semiannual

c. 5.5% compounded monthly Which is the best option of the bank?

3. How long will it take to your money to earn 2000€ at a rate of 12% simple interest rate?

4. If you want to invest only one part of your money, what amount of money will be necessary to accumulate 60,000€ in 6 months at a 9% simple interest rate?

5. You can invest in to projects:

PROJECT A A five-year scope project that consists on an initial investment of 110,000€ and a set of 5 yearly revenues of 25.000€ from year 1 to year 5

PROJECT B A six-year scope project that consists on an initial investment of 100,000€ and a set of 6 yearly revenues of 21.000€ from year 1 to year 6

a) If the cost of capital is 6%, which one would you choose and why?

b) if you only want your money back as soon as is possible. What is the best option?

6. Also, you are thinking in buy your first apartment and use your money as the initial payment. The apartment that you like has a final cost of 350,000€.

a. What is the amount of the rest of the money that you have to pay?

b. You ask for a mortgage scheme for 15 years with an interest rate of 3% compounded monthly. What is the amount of the payments (cashflow) if you start pay at the end of the month?

c. What is the total amount if you ask for a period of mercy, 3 months?

Answer #1

**2]**

Let us say the amount invested is €100

**a]**

Amount received after 5 years = amount invested + (amount invested * interest rate * number of years)

Amount received after 5 years = €100 + (€100 * 8% * 5)

Amount received after 5 years = €140

**b]**

future value = present value * (1 + (r/n))^{nt}

where r = annual interest rate

n = number of compounding periods per year

t = number of years

Amount received after 5 years = €100 * (1 +
(6%/2))^{2*5}

Amount received after 5 years = €134.39

**c]**

future value = present value * (1 + (r/n))^{nt}

where r = annual interest rate

n = number of compounding periods per year

t = number of years

Amount received after 5 years = €100 * (1 +
(5.5%/12))^{12*5}

Amount received after 5 years = €131.57

Option (a) should be chosen as the amount received after 5 years is the highest

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