4.5 a. NOTE: Please show all calculations (no Excel solutions please) to four de

Question

4.5

a.

NOTE: Please show all calculations (no Excel solutions please) to four decimal places if applicable: Jane is 20 years old today. Jane is going to put $1,000 into her savings account on her 21st birthday and again on every birthday for 20 payments (i.e., till her 40th birthday). She will earn 5%, paid annually. How much money will be in the account after she collects her interest and makes her 20th payment?

b.

Calculate how much money she could take out each year for the 20 years from her 41st birthday till her 60th birthday, assuming she still earns 5% and takes out the same amount each year, leaving exactly $0 in the account after removing her 20th payment.

4.5

a.

NOTE: Please show all calculations (no Excel solutions please) to four decimal places if applicable: Jane is 20 years old today. Jane is going to put $1,000 into her savings account on her 21st birthday and again on every birthday for 20 payments (i.e., till her 40th birthday). She will earn 5%, paid annually. How much money will be in the account after she collects her interest and makes her 20th payment?

b.

Calculate how much money she could take out each year for the 20 years from her 41st birthday till her 60th birthday, assuming she still earns 5% and takes out the same amount each year, leaving exactly $0 in the account after removing her 20th payment.

Explanation / Answer

Here we have PMT=$1000, no of payments n=20, i=5% a. Here we have to calculate FV of Ordinary annuity FV of annuity of n=20, PMT=$1000 FVA = PMT(FVIFAi,n) = 1000*(FVIFA5%,20) = 1000*33.06595= $33,065.95 b. Here we have to calculate PMT for n=20, PVA=33065.95 & FV=0 with i=5% PV of annuity of n=20 PVA = PMT(PVIFAi,n) = PMT*(PVIFA5%,20)=PMT*12.4622 = 33065.95 ie PMT = 33065.95/12.4622 = $2,653.30 So she can withdraw $2,653.30 each year from 41st B'day to 60th Bday

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