Figure 5.12 shows that bringing the Kangaroo loan payments forward by 1 year increases their present value from $19.894.82 (as an ordinary annuity) to S21. (as an annuity due). Notice that $21,884.30 = $19,894.82 1.10. 884.30 5.9 Self-Test In Example 5.11 we showed that an annual savings stream of $420.59 invested for 50 years at 10% a year would satisfy a savings goal of $500,000. Suppose instead that you made 50 annual investments, but you made these investments at the beginning of each year rather than at the end. How much would these savings amount to by the end of year 50? You may also want to calculate the future value of an annuity due. If the first cash flow comes immediately, the future value of the cash-flow stream is greater, since each flow has an extra year to earn interest. For example, at an interest rate of 10%, the future value of an annuity due would be exactly 10% greater than the future value of an ordinary annuity. More generally, nf annuity due future value of ordinary annuity x (1 +r) (5.7