{"id":3104,"date":"2021-06-25T13:01:36","date_gmt":"2021-06-25T17:01:36","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=3104"},"modified":"2021-06-29T19:00:29","modified_gmt":"2021-06-29T23:00:29","slug":"videos-average-and-effective-rates","status":"web-only","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/videos-average-and-effective-rates\/","title":{"raw":"Videos: Average and Effective Rates","rendered":"Videos: Average and Effective Rates"},"content":{"raw":"Equivalent: Invest $100 in 2 accounts, the following year they have the same balance<\/em>\r\n\r\nEffective = Average Annual = j1<\/sub><\/em>\r\n\r\nThe humongous bank believes in offering its customers choices. A banker offers you two different options for your investments. The premium growth account offers interest at j2<\/sub> = 10%. The accelerator account offers an effective rate of 10.25%. Which account is better?\r\n\r\n \r\n\r\n[embed]https:\/\/youtu.be\/aLnjZbW3MfU[\/embed]\r\n\r\n \r\n

Using the BAII Plus to convert Interest rates:<\/h2>\r\n[embed]https:\/\/youtu.be\/NQ96SUPWILc[\/embed]\r\n\r\n \r\n\r\nComplete the following table, with each row being equivalent rates:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Effective<\/strong><\/td>\r\nSemi-annual<\/strong><\/td>\r\nQuarterly<\/strong><\/td>\r\nMonthly<\/strong><\/td>\r\n<\/tr>\r\n<\/thead>\r\n
j1<\/sub><\/em> = 12%<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\nj2<\/sub><\/em> = 8%<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\nj4<\/sub><\/em> = 10%<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/td>\r\nj12<\/sub><\/em> = 6%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[embed]https:\/\/youtu.be\/Xr6mEb5Sews[\/embed]\r\n\r\n3. Mortgages charge interest on a semi-annual basis but payments are usually made monthly. Change a mortgage rate of j2<\/sub> = 7% to a rate compounded monthly.\r\n\r\n4. Your credit card charges interest at 1.5% per month. Find the effective rate.\r\n\r\n[embed]https:\/\/youtu.be\/hrMaDlPwn00[\/embed]\r\n\r\n \r\n\r\n5. Premium Savings bonds have the following rates (all annual).\r\n

Year 1: 2% Year 2: 5% Year 3: 12% Year 4: 15% Year 5: 24%<\/p>\r\n(a) How much would a $1,000.00 investment be worth at the end of the fifth year?\r\n\r\n(b) What effective rate was earned?\r\n\r\n[embed]https:\/\/youtu.be\/VkkobvMhWew[\/embed]\r\n\r\n \r\n\r\n \r\n\r\n6. Your investments earn a 100% return in the first year and lose 50% in the second year. What is your effective rate of return over the two years?\r\n\r\n[embed]https:\/\/youtu.be\/8Fob9kInY6A[\/embed]\r\n\r\n \r\n\r\n \r\n\r\n7. A mutual fund had returns of 12% compounded monthly in the first year; 18% compounded annually in the second year; and 4% compounded quarterly in the third year.\r\n\r\nWhat would a $1,000 investment 3 years ago be worth today?\r\nWhat was the average rate (compounded monthly) of return earned?\r\nThe fund lost $100 in the fourth year \u2013 what was the average effective rate of return for the four years?\r\n\r\n[embed]https:\/\/youtu.be\/yiJhxtUl_Ls[\/embed]\r\n\r\n \r\n\r\n \r\n\r\n","rendered":"

Equivalent: Invest $100 in 2 accounts, the following year they have the same balance<\/em><\/p>\n

Effective = Average Annual = j1<\/sub><\/em><\/p>\n

The humongous bank believes in offering its customers choices. A banker offers you two different options for your investments. The premium growth account offers interest at j2<\/sub> = 10%. The accelerator account offers an effective rate of 10.25%. Which account is better?<\/p>\n

 <\/p>\n