John is planning an overseas trip in 3 years. He wishes to save up $25,000 for histrip by investing in an annuity. He has chosen an account that pays 4% p.a.,compounded quarterly.1% 2% 3% 4% 8%3 3.0301 3.0604 3.0909 3.1216 3.24646 6.1520 6.3081 6.4684 6.6330 7.33599 9.3685 9.7546 10.1591 10.5828 12.487612 12.6825 13.4121 14.1920 15.0258 18.977118 19.6147 21.4123 23.4144 25.6454 37.450224 26.9735 30.4219 34.4265 39.0826 66.764830 34.7849 40.5681 47.5754 56.0849 113.283236 43.0769 51.9944 63.2759 77.5983 187.1021Interest RatePeriodFuture values of annuity of $1Use the table of future values of an annuity of $1 above to find the amount that heneeds to invest each quarter to achieve his goal.A $1971.22B $1663.80C $8008.71D $8250.55
Question
John is planning an overseas trip in 3 years. He wishes to save up 1Use the table of future values of an annuity of 1971.22B 8008.71D $8250.55
Solution
To solve this problem, we need to use the Future Value of Annuity table provided.
John's investment is compounded quarterly for 3 years, which means there are 3*4 = 12 periods. The interest rate is 4% per annum, but since it's compounded quarterly, we need to divide it by 4, which gives us 1% per quarter.
Looking at the table, we find the future value factor for 12 periods at 1% interest rate, which is 12.6825.
John wants to save up $25,000. To find out how much he needs to invest each quarter, we divide the total amount he wants to save by the future value factor.
So, 1971.22
Therefore, John needs to invest approximately 1971.22.
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