Question

$1,000 is invested at 5%p.a compounding semi-annually for the first 3 years and at 11% p.a compounding quarterly for the following 5 years. What is the future value at the end of 8 years? (round to nearest dollar; don't include $ sign or commas)

Answer 1

This question is solved by using 'FV' function in Excel or using formula. Function is easier and hence we will use it. First we will calculate the value of the investment at the end of the three years using interest rate of 5% p.a. and semi-annual compounding. This final value will be the principal for the next compounding wherein compounding rate will change to 11% p.a., frequency will be quartely and term will be 5 years.

Syntax of FV function is FV(rate,nper,pmt,[pv],[type]). 'rate' stands for interest rate. Please note that this is the rate for the period. So if the interest is semi-annual, there would be 2 compounding terms in a year and hence interest rate for the single period will be annual percent rate / no. of compounding terms in a year. In our case, since principal of $1,000 is getting compounded semi annually during first three years, rate would be 5%/2 = 2.5%. 'nper' stands for number of periods. Since there are 2 compounding terms in a year in case of semi-annual compounding and in our case first term is of 3 years, total number of periods would be 3*2 = 6. 'pmt' stands for periodic payment. Since there is no annuity in our case, we can consider pmt as 0. 'PV' stands for present value. For our example we will consider PV for the first three years as $1,000. 'type' stands for timing of payment. Since there is no annuity, we will ignore this and keep it as 0. Using this function in excel, our value after 3 years is $1,159.69. This will be our PV for the next 5 years. rate would be 11%/4 = 2.75%. nper would be 5*4 = 20. pmt and type would be 0. Using this function, we will get the future value at the end of 8 years as $1,995.17. Working is as follows:

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