Step 2: Find the PMT for a 25-year

Step 2: Find the PMT for a 25-year ordinary annuity using the FV you just found as the PV. 64,932



160. You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?
a. 7.62%
b. 8.00%
c. 8.40%
d. 8.82%
e. 9.26%


ANS: A
BEGIN Mode
N 24
PV $0
PMT $500
FV $13,000
I/MO 0.63%
I/YR 7.62%


161. Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?
a. 73.67%
b. 77.55%
c. 81.63%
d. 85.93%
e. 90.45%


ANS: E
N 12
rNOM 11.0%
Per. r 0.9167%
PV $72,500
PMT $6,407.67
FV $0 % prin. = Prin2/PMT = 90.45%

Amortization schedule (first 4 months)
Month Beg. Balance Payment Interest Principal Ending Balance
1 72,500.00 6,407.67 664.58 5,743.09 66,756.91
2 66,756.91 6,407.67 611.94 5,795.73 60,961.18
3 60,961.18 6,407.67 558.81 5,848.86 55,112.32
4 55,112.32 6,407.67 505.20 5,902.47 49,209.85


162. On January 1, 2012, your sister's pet supplies business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2012?
a. $17,419.55
b. $17,593.75
c. $17,769.68
d. $17,947.38
e. $18,126.85


ANS: A
Years 30 Nominal r 7.00%
Periods/yr 12 I/period 0.5833%
N (12 mo.) 360 PMT $1,663.26
PV = Loan $250,000 Interest, 2009 $17,419.55
FV $0

Amortization schedule (first 3 months)
Year Beg. Balance Payment Interest Principal End. Balance
1 250,000.00 1,663.26 1,458.33 204.92 249,795.08
2 249,795.08 1,663.26 1,457.14 206.12 249,588.96
3 249,588.96 1,663.26 1,455.94 207.32 249,381.64
4 249,381.64 1,663.26 1,454.73 208.53 249,173.11
5 249,173.11 1,663.26 1,453.51 209.75 248,963.36
6 248,963.36 1,663.26 1,452.29 210.97 248,752.39
7 248,752.39 1,663.26 1,451.06 212.20 248,540.19
8 248,540.19 1,663.26 1,449.82 213.44 248,326.75
9 248,326.75 1,663.26 1,448.57 214.68 248,112.07
10 248,112.07 1,663.26 1,447.32 215.94 247,896.13
11 247,896.13 1,663.26 1,446.06 217.20 247,678.94
12 247,678.94 1,663.26 1,444.79 218.46 247,460.48
19,959.07 17,419.55 2,539.52



163. You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9 more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be to enable you to reach your $50,000 target?
a. $3,008
b. $3,342
c. $3,676
d. $4,044
e. $4,448


ANS: B
We can set up a table with an arbitrary initial deposit that grows at the inflation rate and is then compounded at the nominal rate for (N  t) years. The sum of the compounded amounts should total to $50,000. With an arbitrary initial amount the ending amount is not likely to be $50,000, so we use goal seek as shown in the completed dialog box to find the correct initial deposit.

Inputs:
Years 10
Amount Needed (FV) $50,000
Nominal rate earned on account 5.00%
Inflation 3.00%

1. Goal Seek approach:
Use Goal Seek in the following table to determine the initial deposit. Start with $5,000 as the initial payment, but this will change to $3,341.94.

BOY Payment Computed
Period (t) Initial(1 + I)t Value
0 $3,341.94 $5,443.67
1 $3,442.20 $5,339.98
2 $3,545.47 $5,238.27
3 $3,651.83 $5,138.49
4 $3,761.39 $5,040.62
5 $3,874.23 $4,944.61
6 $3,990.45 $4,850.42
7 $4,110.17 $4,758.03
8 $4,233.47 $4,667.40
9 $4,360.48 $4,578.50
N = 10 $0.00 $50,000.00 = Sum of the 10 compounded values

2. Formula approach:
Find the real rate
1.941748% = (1 + I1572)/(1 + I1573) 1

Find the PV of the required future amount, discounted at the inflation rate. This is our constant dollar future target.
$37,204.70 = I1571/(1 + I1573)(I1570)

Use a calculator or Excel to find the initial payment.
N = 10, I/YR = 1.941748, PV = 0, FV = 37204.70, and set to BEGIN mode.

This is consistent with the Goal Seek solution.
$3,341.94 = PMT(H1593, I1570,0, H1595,1)



164. Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is invested to earn a guaranteed 5% rate of return. If inflation averages 2% per year, how much can she withdraw (to the nearest dollar) at the beginning of each year and keep the withdrawals constant in real terms, i.e., growing at the same rate as inflation and thus enabling her to maintain a constant standard of living?
a. $65,632
b. $72,925
c. $81,027
d. $89,130
e. $98,043


ANS: C
Inputs:
Number of years = 15
Nominal interest rate, rNOM = 5%
A

Kết quả (Việt) 1:

Bước 2: Tìm PMT cho một 25 năm bình thường duy trì hiệu lực sử dụng bệnh viện FV, bạn chỉ cần tìm thấy như PV. 64,932 160. bạn đồng ý để làm cho các trầm tích 24 $500 vào đầu mỗi tháng vào tài khoản ngân hàng. Vào cuối tháng 24, bạn sẽ có $13,000 trong tài khoản của bạn. Nếu ngân hàng của các hợp chất lãi suất hàng tháng, những gì hàng năm lãi suất danh nghĩa sẽ bạn sẽ kiếm?a. 7,62%b. 8,00%c. 8,40%d. 8.82%e. 9,26%ANS: ABắt đầu chế độN 24PV $0PMT $500BỆNH VIỆN FV $13,000TÔI / MO 0,63%TÔI / YR 7,62% 161. doanh nghiệp của bạn chỉ cần lấy ra một khoản cho vay trả góp 1 năm cho $72,500 độ trên danh nghĩa của 11,0% nhưng với bằng các khoản thanh toán cuối cùng của tháng. Những gì tỷ lệ phần trăm của các khoản thanh toán hàng tháng 2 sẽ đi về hướng trả nợ gốc?a. 73.67%b. 77.55%c. 81.63%d. 85.93%e. 90.45%ANS: EN 12 rNOM 11,0% Per. r 0.9167% PV $72,500 PMT $6,407.67 Bệnh viện FV $0% prin. = Prin2/PMT = 90.45%Amortization lịch (tháng 4 đầu)Tháng cầu xin. Số dư thanh toán lãi suất chính kết thúc cân bằng1 72,500.00 6,407.67 664.58 5,743.09 66,756.912 66,756.91 6,407.67 611.94 5,795.73 60,961.183 60,961.18 6,407.67 558.81 5,848.86 55,112.324 55,112.32 6,407.67 505.20 5,902.47 49,209.85 162. ngày 1 tháng 1 năm 2012, con vật cưng của bạn chị em cung cấp kinh doanh thu được một khoản vay thế chấp bình 30 năm cho $250,000 tại một tỷ lệ hàng năm trên danh nghĩa 7,0%, với 360 cuối tháng thanh toán. Công ty có thể khấu trừ lãi suất được trả tiền cho mục đích thuế. Những gì sẽ khấu trừ thuế quan tâm cho năm 2012?a. $17,419.55b. $17,593.75c. $17,769.68d. $17,947.38e. $18,126.85ANS: AYears 30 Nominal r 7.00%Periods/yr 12 I/period 0.5833%N (12 mo.) 360 PMT $1,663.26PV = Loan $250,000 Interest, 2009 $17,419.55FV $0 Amortization schedule (first 3 months)Year Beg. Balance Payment Interest Principal End. Balance1 250,000.00 1,663.26 1,458.33 204.92 249,795.082 249,795.08 1,663.26 1,457.14 206.12 249,588.963 249,588.96 1,663.26 1,455.94 207.32 249,381.644 249,381.64 1,663.26 1,454.73 208.53 249,173.115 249,173.11 1,663.26 1,453.51 209.75 248,963.366 248,963.36 1,663.26 1,452.29 210.97 248,752.397 248,752.39 1,663.26 1,451.06 212.20 248,540.198 248,540.19 1,663.26 1,449.82 213.44 248,326.759 248,326.75 1,663.26 1,448.57 214.68 248,112.0710 248,112.07 1,663.26 1,447.32 215.94 247,896.1311 247,896.13 1,663.26 1,446.06 217.20 247,678.9412 247,678.94 1,663.26 1,444.79 218.46 247,460.48 19,959.07 17,419.55 2,539.52 163. You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9 more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be to enable you to reach your $50,000 target?a. $3,008b. $3,342c. $3,676d. $4,044e. $4,448ANS: BWe can set up a table with an arbitrary initial deposit that grows at the inflation rate and is then compounded at the nominal rate for (N  t) years. The sum of the compounded amounts should total to $50,000. With an arbitrary initial amount the ending amount is not likely to be $50,000, so we use goal seek as shown in the completed dialog box to find the correct initial deposit.Inputs:Years 10Amount Needed (FV) $50,000Nominal rate earned on account 5.00%Inflation 3.00%1. Goal Seek approach: Use Goal Seek in the following table to determine the initial deposit. Start with $5,000 as the initial payment, but this will change to $3,341.94. BOY Payment Computed Period (t) Initial(1 + I)t Value 0 $3,341.94 $5,443.67 1 $3,442.20 $5,339.98 2 $3,545.47 $5,238.27 3 $3,651.83 $5,138.49 4 $3,761.39 $5,040.62 5 $3,874.23 $4,944.61 6 $3,990.45 $4,850.42 7 $4,110.17 $4,758.03 8 $4,233.47 $4,667.40 9 $4,360.48 $4,578.50 N = 10 $0.00 $50,000.00 = Sum of the 10 compounded values 2. Formula approach: Find the real rate 1.941748% = (1 + I1572)/(1 + I1573) 1 Find the PV of the required future amount, discounted at the inflation rate. This is our constant dollar future target. $37,204.70 = I1571/(1 + I1573)(I1570) Use a calculator or Excel to find the initial payment. N = 10, I/YR = 1.941748, PV = 0, FV = 37204.70, and set to BEGIN mode. This is consistent with the Goal Seek solution. $3,341.94 = PMT(H1593, I1570,0, H1595,1)



164. Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is invested to earn a guaranteed 5% rate of return. If inflation averages 2% per year, how much can she withdraw (to the nearest dollar) at the beginning of each year and keep the withdrawals constant in real terms, i.e., growing at the same rate as inflation and thus enabling her to maintain a constant standard of living?
a. $65,632
b. $72,925
c. $81,027
d. $89,130
e. $98,043


ANS: C
Inputs:
Number of years = 15
Nominal interest rate, rNOM = 5%
A