Which of the following is not a circumstance in which the number of payments, n, is the unknown value to be calculated? Multiple choice question. Determining the time required for a periodic savings plan to reach a savings goal. Determining how long a single investment can sustain periodic withdrawals. Determining the time required for periodic payments to pay off a loan. Determining the amount that must be saved each period to reach a savings goal.
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An ordinary annuity is an account in which you make a fixed deposit at the end of each compounding period. You want to use an annuity to help you save money for college. The formula t = n * In(Sr + Pn) gives the time t (in years) required to have S dollars in the annuity if your periodic payments P (in dollars) are made n times a year and the annual interest rate is r (in decimal form). In[(Sr + Pn) * (Pn) * (n + r)] is the expansion of the formula. True b. False
Ashish T.
Consider an account with an APR of 5.6%. Find the APY with quarterly compounding, monthly compounding, and daily compounding. Comment on how changing the compounding period affects the annual yield. Suppose someone wants to accumulate $130,000 for retirement in 30 years. The person has two choices. Plan A is a single deposit into an account with annual compounding and an APR of 8%. Plan B is a single deposit into an account with continuous compounding and an APR of 7.8%. How much does the person need to deposit in each account in order to reach the goal? Find the savings plan balance after 2 years with an APR of 3% and monthly payments of $200. Suppose that on January 1 you have a balance of $4200 on a credit card whose APR is 16%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1. a. Calculate your monthly payments. b. When the card is paid off, how much will you have paid since January 1? c. What percentage of your total payment from part (b) is interest? Assume you have a balance of $1000 on a credit card with an APR of 18%, or 1.5% per month. You start making monthly payments of $200, but at the same time you charge an additional $100 per month to the credit card. Assume that interest for a given month is based on the balance for the previous month. The following table shows how you can calculate your monthly balance. Complete and extend the table to show the balance at the end of each month until the debt is paid off. How long does it take to pay off the credit card debt?
Madhur L.
In Question 10, you figured out the periodic rate (interest per month) by dividing the APR by 12, the number of times the interest is being compounded in one month. In Question 11, to find the account balance after 24 months, you used 24 months in the exponent. In the next problem, we want to develop a general formula to calculate the value of any CD. Let P = the principal, r = the annual interest rate (APR) as a decimal, n = the number of compounding periods in a year (1 for annual, 12 for monthly, 52 for weekly, etc.) t = number of years. So in the previous two questions, n = 12, since we were compounding monthly (12 times per year). Think about how you answered the last question: how did you find the interest rate per period? To find the value after 3 years, how did you figure out the number of months? Question 12 Write a general formula that can be used to calculate the value of any CD, using the variables defined above (P, t, r, and n). A = Hint: If you get stuck, we'll provide some hints
Adi S.
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