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Pay nothing for 11 months. Then pay ​$1653​, followed by 19 more $1653 payments every 6months...

Pay nothing for 11 months. Then pay ​$1653​, followed by 19 more $1653 payments every 6months after that. At 5.3% APY​ (effective annual​ rate), what is the combined present value of all these 20 ​payments? (Rounded to the nearest​ dollar.)

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Answer #1

Semi Annual rate =5.3%/2 =2.65%
Value of Payment at end of year 1 using annuity due formula =(1+r)*PMT*(1-(1+r)^-n)/r)
=(1+2.65%)*1653*(((1-(1+2.65%)^-20)/2.65%)=26080.7885

PV of all these combined payments =26080.7885/(1+5.3%)^1 =24768.08 or 24768

Another PV could be =26080.7885/(1+5.3%/12)^12=24737.39

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