Question of mathematics (general mathematics course Australia HSC)?
Jerry spends $ 5000 on an investment of 7.2% annual interest compounded annually over a period of 10 years. Tom did not have $ 5000, but intends to invest $ 1000 each year into an annuity for 10 years, also pays 7.2% annual interest compounded annually. Comparing the current values, determine that the investment will secure the greatest financial benefit? Please support which had many discussions with my math teacher about it lol
Jerry received for each $ 1000 invested a lot more interest than interest, so must have the best interest of the average. In detail: the return of Jerry: 5000 * (1 +7.2 / 100) ^ 10 = 10,021.16 Tom Return: 1000 * [(1 +7.2 / 100) ^ 10 + (1 +7.2 / 100) ^ 9 + .. + (1 +7.2 / 100)] = 1000 * (1.072 + 1.072 ^ 2 +.. + 1.072 ^ 10) = 1000 * [(1.072 ^ 11 - 1) / (1.072 - 1) -- 1] = 14,951.89 But 10,000 total invested Tom and Jerry Only 5000. Calculation of average interest: Jerry: Years of $ 1000: 5 * 10 = 50 = Jerry acquired 10021,16-5000 5021.16 earned each year on average $ 1000: 5021.16/50 = 100.423, which is a weighted average interest of 10.0423% Tom: Years of $ 1000: (10 9 + .. 1) = 55 Tom won 14,951.89 to 10,000 = 4951.89 won per year averaged $ 1000: 4951.89 / 55 = 90.034, an average interest of 9.0034% So, Jerry has the best interest of the average.
Related posts:
Comments on this entry are closed.