Question

Two standard savings accounts, A and B, have an AER of 3%. Account A pays interest every quarter, and Account B every month. Work out whether the interest paid at the end of the year is higher for Account A, for Account B or the same for both accounts, assuming the same amount was invested in each account initially

Answer 1

Answer:

Assuming that the amount deposited is 100.

Account A (interest every quarter):

Compounding interest=P(1+AER/400)⁴

=100(1+3/400)⁴=103.033

Interest paid at the end of year 1= 103.033-100=3.033

or alternatively

Int. paid at the end of first quarter=100*3*(3/12)/100=0.75.

Int. paid at the end of second quarter=100.75*3*(3/12)/100=0.755

Int. paid at the end of third quarter=101.505*3*(3/12)/100=0.761

Int. paid at the end of year=102.266*3*(3/12)/100=0.767.

Total interest paid at the end of year=0.75+0.755+0.761+0.767=3.033.

Account B (interest every month):

Compounding interest=P(1+AER/1200)¹²

=100(1+3/1200)¹²=103.041

Total interest paid at the end of year=103.041-100=3.041.

Interest paid in Account B is higher than the interest paid in Account A.