Question

An annuity immediate with annual payments has an initial payment of 1. Subsequent payments increase by 1 until reaching a payment of 10. The next payment after the payment of 10 is also equal to 10, and then subsequent payments decrease by 1 until reaching a final payment of 1. Determine the annual effective interest rate at which the present value of this annuity is 78.60.

(A) .0325 (B) .0335 (C) .0345 (D) .0355 (E) .0365

Answer 1

Answer>

The annual effective interest rate should be equal to 3.35% = .0335, hence option (B)

Please refer to the below images. I have calculated the annual effective rate of interest in excel by using the goal seek functionality under what-if analysis tool, present under data tab.

Column 1 refers to the year (n) , starting from 1, Column 2 is the annual payment (P), Column 3 is the present value of each payments, given by P/((1+r)^n). Cell D2 is the rate (r), which we need to calculate.

HOME INSERT PAGE LAYOUT FORMULAS DATAREVIEW VIEW Connections Properties Clear A From Access From Web b From Text oces Z A From Other Existing Refresh Sort Filter Reapply Text to Flash Remove Data Consolidate What-If Analysis Advanced Columns ill Duplicates Validation nnections AllEdit Links Get External Data Connections Sort & Filter Data Tools 1 Year Payment PV Rate 0.9681 3.35% 2 1.872 3 2.718 4 3.506 54.240 4.924 7 5.558 6.146 6.690 7.193 106.959 9 6.060 8 5.212 7 4.413 3.660 5 2.951 42.284 3 1.658 2 1.069 1 0.517 110 78.600 4 Goal Seek Status Goal Seeking with Cell C22 found a solution. Target val 78.6 Current value: 78.600 10 10 10 OK Cancel 13 16 17 18 19 20 12 13 14 15 16 17 18 19

Hope this answers your question.