Charlie has deposited $50,000 annually every January 1 since 2008 into a retirement fund that earns a 5% effective annual rate of interest. He plans...

• Charlie has deposited $50,000 annually every January 1 since 2008 into a retirement

fund that earns a 5% effective annual rate of interest. He plans to retire at the end

of December 2047. Then he plans to withdraw a xed amount at the end of each

month starting in January 2048 for 30 years, at which time the account balance

will be reduced to zero.

(a) How much will Charlie accumulate as of 31 December 2047?

(b) How much will he be able to withdraw each month?

(c) How much total interest will he earn throughout the 70-year span?

• Megan needed a loan of $1,000,000 to expand her business. On last Monday (23

July 2018) she went to the bank, and the bank lent her the money at a 10% effective

annual interest rate, which she agreed to pay back in ve equal annual installments

of K starting on 23 July 2021, plus an extra payment of $150,000 on 23 July 2022

and another of $200,000 on 23 July 2024.

(a) Find the value of K.

(b) How much interest will she pay?

(c) Find the outstanding loan balance at 31 December 2022.

(d) Find the principal repaid on 23 July 2023.

(e) Find the amount of interest paid in the last installment.

• A certain bond is going to be redeemed at par on 31 December 2022 and bears a

coupon rate at 8% per annum payable semiannually on 30 Jun and 31 Dec. Find

the highest price that an investor is willing to pay today (27 July 2018) for the

bond if has an opportunity cost of 7.50% annually.

• Let It be the annual yield rate of a fund for the t-th year. The yield rates in

different years are independently distributed. Suppose that I1 will be 7%, 7.5%,

8% or 8.5% with probabilities 0.15, 0.20, 0.25 and 0.40, respectively, and I2 will be

equally likely to be 7%, 7.5%, 8% or 8.5%. If you invest $30,000, compute:

(a) the expected accumulated value after two years,

(b) the variance of the accumulated value after two years,

(c) the probability that the accumulated value after two years will be lower than

$35,000.

• Mr. X deposits $10,000 today and another $10,000 in ve months into a fund

paying simple interest of 1% per month. Mrs. Y will make the same two deposits,

but the rst $10,000 will be deposited n months from today and the second $10,000

will be deposited 2n months from today in a fund paying compound interest. Mrs.

Y's deposits earn a monthly effective rate of 0.9%. At the end of a year, the

accumulated amount of Mrs. Y's deposits equals the accumulated amount of Mr.

X's deposits. Find n.