Question

QUESTION 7

What's the present value of $100,000 discounted back 10 years if the appropriate interest rate is 6.5%, compounded quarterly?

QUESTION 13

Suppose you inherited $500,000 and invested it at 6.25% per year. How much could you withdraw at the end of each of the next 35 years?

QUESTION 19

Suppose you borrowed $75,000 at a rate of 12% and must repay it in equal annual installments at the end of each of the next 5 years.

1. How much principal did you pay off during the first year?

2. How much interest would you have to pay during the second year?

3. How much would you still owe after the 4th year?

please answer all questions directly to chegg and show work

Answer 1

(7) Future Value = $ 100000, Discount Rate = 6.5 % per annum or (6.25/4) = 1.625 % per quarter

Time Period = 10 Year or 40 quarters

Therefore, Present Value = 100000 / (1.01625)^(40) = $ 52478.046

(13) Inheritance = $ 500000, Investment Rate = 6.25 % and Time Period = 35 years

Now, if 35 equal annual withdrawals are made at the end of each year, then the total present value of all those withdrawals should equal the current inheritance of $ 500000

Let the equal annual withdrawals be $ K

Therefore, 500000 = K x (1/0.0625) x [1-{1/(1.0625)^(35)}]

K = $ 35503.63215

(19) Borrowing = $ 75000, Rate of Interest = 12 % and Borrowing Period = 5 years.

The five equal annual installments should have a total present value equal to the initial borrowing of $75000, discounted at the interest rate of 12 %.

Let the equal annual installments be $ K

Therefore, 75000 = K x (1/0.12) x [1-{1/(1.12)^(5)}]

K = $ 20805.7299

The principal paid off in Year 1 is equal to the difference between the annual installment paid at the end of Year 1 and the interest accrued for Year 1 on the loan amount outstanding at the beginning of Year 1. The same principle would be applicable for all year subsequent to that.

Principal Outstanding at the beginning of Year 1 = Original Borrowing = $ 75000

Interest Accrued = 12 % of 75000 = 0.12 x75000 = $ 9000

Principal Paid Off = 20805.7299 - 9000 = $ 11805.7299

Interest Payable during the second year would be equal to the interest accrued on the principal (loan) outstanding at the beginning of Year 2.

Principal Outstanding at the beginning of Year 2 = Original Loan - Principal Paid off at the end of Year 1 = 75000 - 11805.7299 = $ 63194.2701

Interest Accrued in Year 2 = 12 % of 63194.2701 = 0.12 x 63194.2701 = $ 7583.312412

The amount owed (principal outstanding) at the end of Year 4 will be equal to the present value at the end of Year 4 of the remaining annual installment discounted at the rate of interest of 12 %

Amount Owed at the end of Year 4 = 20805.7299 / 1.12 = $ 18576.54455