1. Find the monthly payment that will yield the future valueof $105,000 using an
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Question
1. Find the monthly payment that will yield the future valueof $105,000 using an ordinary annuity at 9.5% interest for34 years. (Round the answer to thenearest cent.)2. Susan and Bill Stamp want to set up a TDA that willgenerate sufficient interest at maturity to meet their livingexpenses, which they project to be $1,200 per month. (a) Find the amount needed at maturity togenerate $1,200 per month interest, if they can get 7.25% interestcompounded monthly. (Round the answer to the nearest cent.)
$
(b) Find the monthly payment that they would have to make into anordinary annuity to obtain the future value found in part (a) iftheir money earns 9.75% and the term is 25 years. (Round the answerto the nearest cent.)
$ 1. Find the monthly payment that will yield the future valueof $105,000 using an ordinary annuity at 9.5% interest for34 years. (Round the answer to thenearest cent.)
2. Susan and Bill Stamp want to set up a TDA that willgenerate sufficient interest at maturity to meet their livingexpenses, which they project to be $1,200 per month. (a) Find the amount needed at maturity togenerate $1,200 per month interest, if they can get 7.25% interestcompounded monthly. (Round the answer to the nearest cent.)
$
(b) Find the monthly payment that they would have to make into anordinary annuity to obtain the future value found in part (a) iftheir money earns 9.75% and the term is 25 years. (Round the answerto the nearest cent.)
$ (a) Find the amount needed at maturity togenerate $1,200 per month interest, if they can get 7.25% interestcompounded monthly. (Round the answer to the nearest cent.)
$
(b) Find the monthly payment that they would have to make into anordinary annuity to obtain the future value found in part (a) iftheir money earns 9.75% and the term is 25 years. (Round the answerto the nearest cent.)
$
Explanation / Answer
1. Ordinary annuity for N=34 yrs which will pay I=9.5%pa. FVA = 105000 Here FVA = PMT(FVIFAi,n). PMT is to be found & on monthly basis. So no ofperiod n = N*12 = 34*12 = 408. i = I/12 = 9.5%/12 = 0.79 %.FVIFAi,n = [(1+i)^n-1]/i. So FVA = 105000 = PMT*[(1+0.79%)^408 - 1]/0.79% =PMT*23.79/0.79% = 3011.7 * PMT SO PMT = 105000/3011.7 = 34.86 So Monthly payment of $34.86 will yield an annuity of $105000after 34 Yrs at 9.5%
2. A. This is case of Perpetuity. Perpetuity = PMT/i PMT = 1200 pm * 12 = 14400 annualy Int i= 7.25% compounded monthly
So Perpetuity = 14400/7.25% = $198,620.67
2B. Ordinary annuity for N=25 yrs which will pay I=9.75%pa. FVA = 105000 Here FVA = PMT(FVIFAi,n). PMT is to be found & on monthly basis. So no ofperiod n = N*12 = 25*12 = 300. i = I/12 = 9.75%/12 = 0.8125%.
FVIFAi,n = [(1+i)^n-1]/i. So FVA = 105000 = PMT*[(1+0.8125%)^300 - 1]/0.8125% =PMT*10.33/0.8125% = 1271.66 * PMT SO PMT = 105000/1271.66 = 82.57 So Monthly payment of $82.57 will yield an annuity of $105000after 25 Yrs at 9.75%
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