Question

Question 3 Alex and Anna each need £10 per week to live on. They decide to ask their dad for a weekly allowance. Alex agrees that she will receive £10 each week for one year (52 weeks). Anna noted from FT.com that she could receive 3% per annum effective interest if she put money into a savings account and then took out the £10 from the account each week. She therefore asks for £500 at the start of the year instead. The first £10 (i.e. paid to Alex and paid out by Anna) is at the end of the first week. (a) Does Anna end the year in surplus or does she run out of money? (4 marks] (b) If she does have a surplus how much would it be at the end of the year? [1 marks] [Total: 5 marks]

Can anyone help me with this annuity question?!

Answer 1

The questions you have asked are the below answers:

a) Anna will run out of money at the end of the year. As the total live on amount required for whole year is 520 Eurs.

But if we calculate the interest then we are getting 515 Eurs with 3% interest rate. Please find the below calculation for the Deposit amount at the end of the year.

Principal * Interest Rate * Period = Simple Interest

500 * 3% * 1 year = 15

So the final amount received from the bank after interest rate is 515 Eurs, whereas money needed for the live on by Anna in a year is 520 Eurs. That means she will be shortage of 5 Eurs.

b) Anna will not be having any surplus amount by end of the year. As per the interest rate formula she will be shortage of 5 Eurs.