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Calculate the future value of an ordinary annuity consisting of monthly payments of $470\$470 for five years. The rate of return was 9.3%9.3\% compounded monthly for the first two years, and will be 7.2%7.2\% compounded monthly for the last three years. (Do not round intermediate calculations and round your final answer to 22 decimal places.) Future value

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Q. Calculate the future value of an ordinary annuity consisting of monthly payments of $470\$470 for five years. The rate of return was 9.3%9.3\% compounded monthly for the first two years, and will be 7.2%7.2\% compounded monthly for the last three years. (Do not round intermediate calculations and round your final answer to 22 decimal places.) Future value
  1. Calculate FV first two years: Calculate the future value of the annuity for the first two years with a 99.33% annual interest rate compounded monthly.\newlineWe have:\newlineMonthly payment (PMT) = $470\$470\newlineNumber of payments for the first two years (n) = 22 years ∗12* 12 months/year = 2424 months\newlineMonthly interest rate (i) = 9.3%9.3\% annual rate / 1212 months = 0.093/120.093 / 12\newlineFuture value of an annuity formula: FV=PMT×(((1+i)n−1)/i)FV = PMT \times (((1 + i)^n - 1) / i)\newlineLet's calculate the future value for the first two years:\newlineFV_first_two_years=470×(((1+0.093/12)24−1)/(0.093/12))FV\_{first\_two\_years} = 470 \times (((1 + 0.093/12)^{24} - 1) / (0.093/12))
  2. Accumulated value first two years: Calculate the accumulated value of the annuity for the first two years.\newlineFVfirst two years=470×((1+0.09312)24−1)/(0.09312)FV_{\text{first two years}} = 470 \times \left(\left(1 + \frac{0.093}{12}\right)^{24} - 1\right) / \left(\frac{0.093}{12}\right)\newlineFVfirst two years≈470×((1+0.00775)24−1)/0.00775FV_{\text{first two years}} \approx 470 \times \left(\left(1 + 0.00775\right)^{24} - 1\right) / 0.00775\newlineFVfirst two years≈470×(1.19985−1)/0.00775FV_{\text{first two years}} \approx 470 \times \left(1.19985 - 1\right) / 0.00775\newlineFVfirst two years≈470×(0.19985/0.00775)FV_{\text{first two years}} \approx 470 \times \left(0.19985 / 0.00775\right)\newlineFVfirst two years≈470×25.7871FV_{\text{first two years}} \approx 470 \times 25.7871\newlineFVfirst two years≈$12,119.94FV_{\text{first two years}} \approx \$12,119.94
  3. Calculate FV last three years: Calculate the future value of the annuity for the last three years with a 7.2%7.2\% annual interest rate compounded monthly.\newlineWe have:\newlineMonthly payment (PMT) = $470\$470\newlineNumber of payments for the last three years (n) = 33 years ∗12* 12 months/year = 3636 months\newlineMonthly interest rate (i) = 7.2%7.2\% annual rate / 1212 months = 0.072/120.072 / 12\newlineFuture value of an annuity formula: FV=PMT×(((1+i)n−1)/i)FV = PMT \times (((1 + i)^n - 1) / i)\newlineLet's calculate the future value for the last three years:\newlineFV_last_three_years=470×(((1+0.072/12)36−1)/(0.072/12))FV\_{last\_three\_years} = 470 \times (((1 + 0.072/12)^{36} - 1) / (0.072/12))
  4. Accumulated value last three years: Calculate the accumulated value of the annuity for the last three years.\newlineFV_last three years=470×((1+0.07212)36−1)/(0.07212)FV\_{\text{last three years}} = 470 \times \left(\left(1 + \frac{0.072}{12}\right)^{36} - 1\right) / \left(\frac{0.072}{12}\right)\newlineFV_last three years≈470×((1+0.006)36−1)/0.006FV\_{\text{last three years}} \approx 470 \times \left(\left(1 + 0.006\right)^{36} - 1\right) / 0.006\newlineFV_last three years≈470×(1.243449−1)/0.006FV\_{\text{last three years}} \approx 470 \times \left(1.243449 - 1\right) / 0.006\newlineFV_last three years≈470×(0.243449/0.006)FV\_{\text{last three years}} \approx 470 \times \left(0.243449 / 0.006\right)\newlineFV_last three years≈470×40.57483FV\_{\text{last three years}} \approx 470 \times 40.57483\newlineFV_last three years≈$$FV\_{\text{last three years}} \approx \$\$1919,070070.0707\)
  5. Calculate total FV: Calculate the total future value of the annuity by adding the future value of the first two years to the future value of the last three years.\newlineWe have:\newlineFVfirst two years≈$12,119.94FV_{\text{first two years}} \approx \$12,119.94\newlineFVlast three years≈$19,070.07FV_{\text{last three years}} \approx \$19,070.07\newlineTotal future value (FVtotalFV_{\text{total}}) = FVfirst two years+FVlast three yearsFV_{\text{first two years}} + FV_{\text{last three years}}\newlineFVtotal≈$12,119.94+$19,070.07FV_{\text{total}} \approx \$12,119.94 + \$19,070.07
  6. Final total FV: Calculate the final total future value of the annuity.\newlineFVtotal≈$(12,119.94)+$(19,070.07)FV_{\text{total}} \approx \$(12,119.94) + \$(19,070.07)\newlineFVtotal≈$(31,190.01)FV_{\text{total}} \approx \$(31,190.01)

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