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2.Which simple interest rate per year over a six-year time span is closest to being equivalent to the following: an effective rate of discount of 3% for the first year, an effective rate of discount of 6% for the second year, an effective rate of discount of 9% for the third year, and an (annual) effective rate of interest of 5% for the fourth, fifth and sixth years?
3.A lender will provide one-year loans at an annual effective interest rate of 10% to borrowers who are deemed to be without risk of default. The lender has identified a class of risky borrowers who may default partially. In the case of default, the lender can recover 40% of the principal amount. The lender has determined that if he set an annual effective interest rate of 15% to this class of risky borrowers, his expected return would be the same as that from lending to the risk-free borrowers. Calculate the chance that a risky borrower from this class will default.
4.Jennifer needs $500 cash for an emergency. She decides to take a 14-day payday loan from a private lender that charges a fee equivalent to an APR of 440%. Jennifer’s friend Steven is closing on his condo purchase, and also finds himself short of $500 for his down payment. Steven decides to take a credit card cash advance — a cash loan from his credit card issuer. His credit card compounds interest daily at a cash advance APR of 23%. In addition, the card charges a $10 fixed fee for each cash advance transaction. What is the maximum number of days Steven can hold the cash advance, if he does not want to pay more interest and fees than Jennifer? Choose the closest value. (Assume a year has 365 days.)
5. Chuck needs to purchase an item in 10 years. The item costs 200 today, but its price inflates at 4% per year. To finance the purchase, Chuck deposits 20 into an account at the beginning of each year for 6 years. He deposits an additional X at the beginning of years 4, 5, and 6 to meet his goal. The annual effective interest rate is 10%. Calculate X.
On January 1 of Year 1, Brian opens an investment account where interest is credited at a nominal interest rate of 8% convertible quarterly. Brian deposits $1000 at account opening and $100 at the beginning of every subsequent month (i.e. starting from February, Year 1). On April 1 of every year, Brian makes a tax payment from this account on his interest income. The tax is calculated as 25% of the total interest earned in the previous calendar year. (A calendar year is a one-year period between January 1 and December 31.) Brian has no other source of interest income, and did not receive any interest prior to opening this investment account.
Answer questions 6-8 based on the information above. All numerical solutions must be rounded to the nearest two decimal places. Any rate’s accuracy is based on percentage and therefore the number itself should be accurate to the fourth decimal place (e.g. 0.0123 or 1.23%). To preserve accuracy, do not round until the last step or use at least 4 decimal places for monetary amount and 6 decimal places for rates in your calculation process.
6. What effective monthly discount rate is equivalent to the 8% nominal interest rate of Brian’s account? Enter your answer as a decimal (e.g. 1.23% should be entered as 0.0123).
7.Calculate Brian’s interest tax payment in Year 2. (Note that this is for the interest income in Year 1.)
8.Calculate Brian’s account balance at the end of Year 2
