Question

An amount of 10 000 was invested in a special savings account on 15 May at an interest rate of 15% per annum compounded quarterly for 7 months. Interst is calculated on 1 January, 1 April, 1 July and 1 October every year. If the simple is used for the odd periods and compound interest for the rest of the term, the amount of interest received after 7 months equals?? 1) 665.54 2) 896.95 3) 901.35 4) 1644.57 5) None of the above And if fractional compounding is used for the full term of 7 months, the total amount of interest received will equal? 1) 829.79 2) 894.04 3) 898.43 4) 901.73 5) None of the above

Answer 1

15% per annum is 3.75% per quarter. 15 May is included in the 2nd quarter of the year, an even period. At the end of the quarter 10000 would accumulate a whole quarter's interest: 375, making the total savings 10375. This is the starting amount for July, so by October, if the simple interest is calculated on the original 10000 a further 375 would accumulate making the savings 10750. October is the start of the last quarter and the 7-month period ends in December. 10750 would accumulate by compound interest, becoming 11153.125 at the end of the quarter. So the interest is 1153.13.

If compound interest is applied for the whole 7 months, then taking this to be 3 quarter periods, the interest is 1167.71. If simple interest is applied for 7 months the interest is 875, based on 7/12*0.15*10000.