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Starting six months after her grandson Robin's birth, Mrs
Starting six months after her grandson Robin's birth, Mrs. Devine made deposits of $210 into a trust fund every six months until Robin was eighteen years old. The trust fund provides for equal withdrawals at the end of each six months for five years, beginning six months after the last deposit. If interest is 4.23% compounded semi-annually, how much will Robin receive every six months? Robin will receive $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
Expert Solution
Amount deposit each 6 month period (P)=210
number of 6 month period in 18 years (n) =18*2 = 36
interest rate per 6 month period = annual rate/period in year
=4.23%/2 =0.02115
Amount accumulated at time of 18 years at end of deposit period will be calculated by future value of annuity formula
future value of annuity formula = P*(((1+i)^n)-1)/i
=210*(((1+0.02115)^36)-1)/0.02115
=11163.63402
This is value of annuity for future withdrawals
Now it is present value (PV)=11163.63402
number of 6 monthly withdrawal in 5 year period (n) =5*2 =10
nterest rate per 6 month period=4.23%/2 =0.02115
Robin will receive equal annuity from fund
equal or annuity Payment formula = PV* i *((1+i)^n)/((1+i)^n-1)
11163.63402*0.02115*((1+.02115)^10)/(((1+.02115)^10)-1)
=1250.298248
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