NENT FOUR For the following problem, give answers correct to five significant figures for calculations of R in your answers be sure to define annuities and perpetuities in context. a. b.

For an investment of $550 000, an annuity with an interest rate of 5.39% p.a. will give a greater monthly payment than a perpetuity with an interest rate of 5.4% p.a. Assume that the annuity will last 20 years. Compare an annuity and perpetuity: compare the two options, suggest which option is better, include calculations and justify your answer. A housing loan of $380 000 is taken out for 15 years. Interest is charged at 9% per annum adjusted (compounded) monthly. The debt is to be repaid in monthly instalments. Complete the amortisation table for the first five months, assuming $3854 is paid each month. Payment Number Payment Made Interest Paid ($) ($) 0.00 0.00 3854.00 n 241 0 1 2 3 4 5 Total Principal Reduction ($) 0.00 Balance Remaining (5) 380 000.00 378 996.00