Question Description
I'm working on a mathematics multi-part question and need an explanation and answer to help me learn.
Assume Mr. Smith has reached retirement and has $250,000 in an account which is earning 6.5%. He would now like to make equal monthly withdrawals for the next 15 years to completely deplete this account. Find the withdrawal payment.
A ten-year $1,000 bond pays $35 every six months. If the current interest rate is 8.2%, find the fair market value of the bond.
- Hint: You must do the following.
- Find the present value of $1000.
Find the present value of the $35 payments.
The fair market value of the bond = a + b
- An amount of $200,000 is borrowed for 5 years at a rate of 12%. Make an amortization schedule showing the quarterly payment, the quarterly interest on the outstanding balance, the portion of the payment going toward reducing the debt, and the balance.
- Jane plans to buy a house in 10 years. The house she dreams about costs about $150,000 today. The cost of houses increases at 2.5% per year.
- How much will the house cost in ten years?
Jane currently has $75,000 that she can invest to earn 3% interest over the next ten years. How much will Jane accumulate from her investment of 75,000 Dollars in ten Years?
- How much additional money would Jane need in ten years? In effect, how much money does Jane need to borrow to purchase her house?
- Prepare an amortization table to pay off Janeβs mortgage, if she can borrow at an annual rate of 6.5% to pay off the mortgage quarterly in 5 years after buying the house
Explanation & Answer
View attached explanation and answer. Let me know if you have any questions.
Questions :
1. Assume Mr. Smith has reached retirement and has $250,000 in an account which is
earning 6.5%. He would now like to make equal monthly withdrawals for the next
15 years to completely deplete this account. Find the withdrawal payment.
Answer 1 :
Using the Formula PV = πππ[1 β
π βππ‘
π
π
π
(1+ )
]
We need to calculate PMT, with PV = $250,000 & r = 0.065, with n = 12 months and t = 15
years. Giving the following :
250000= πππ[1 β
(1+
0.065 β12.15
)
12
0.065
12
]
250000
Hence : PMT = 114.802 = $2177.77 ππΌππ»π·π
π΄ππ΄πΏ ππ΄πππΈππ.
2. A ten-year $1,000 bond pays $35 every six months. If the current interest rate is
8.2%, find the fair market value of the bond.
Answer 2 :
Number of installment = 10 years * 2 Payments every year = 20.
Calculating the PV of maturity = FV/(1+ * r)^t = 1000/(1+0.082)^20
= 1000/4.8366 = $206.75
=> Present value of bon interest : Current Interest * PV(AF)
= (35/1.082+1)+ (35/1.082+1)^2 +β¦ + (35/1.082+1)^20 = 35*0.924*(1-0.206/1-0.924)
= $337.63
Meaning the fair value of bond = PV of Markets ...