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Problem 5 - Annuities with Block Payments & Perpetuities Michael made the following deposits in a...

Problem 5 - Annuities with Block Payments & Perpetuities

Michael made the following deposits in a fund paying annual effective rate of interest of 5.1%:


(i) $70 at the beginning of years 1 - 13
(ii) No deposits at the beginning of years 14 - 18
(iii) $120 at the beginning of years 19 - 37.

How much did Michael accumulate at the end of 37 years?

AV=

math   Statistics-And-Probability   
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Answer #1

Solution: Effective annual interest rate-i 5.1%--0.051 For an amount P invested for T period of time at an interest rate of i, the final accumulated amount is Amount accumulated at the end of 37 years is equal to the amount accumulated at the beginning of 38th year Amount Invested 70 70 70 70 70 70 70 70 70 70 70 70 70 0 Amount Accumulated at the end of 37 years 70х(1+0.051)л(38-1-440.96 70x(1+0.051)^(38-2) 419.56 70x(1+0.051)/(38-3) 399.2 70x(1+0.051)A(38-4) 379.83 70х(1+0.051)^(38-5) 3614 70х(1+0.051)л(38-6) 343.86 70х(1+0.051)л(38-7) 327.18 70x(1+0.051)/(38-8) 311.3 70х(1+0.051)^(38-9) 296.19 70x(1+0.051)A(38-10) 281.82 70х(1+0.051)л(38-11)-268.15 70х(1+0.051)(38-12) 255.13 70x(1+0.051)/(38-13)-242.75 Ох(1+0.051)(38-14) 0 0x(1+0.051)A(38-15) 0 0x(1+0.051)A(38-16) 0 0x(1+0.051)A(38-17) 0 Ох(1+0.051)(38-18)-0 Beginning of Year 2 4 6 8 10 12 13 14 15 16 17 18 0 0

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