You have a choice of two investment accounts. Investment A is a 15-year annuity that features end-of-month $1,200 payments and has an interest rate of 8.5 percent compounded monthly. Investment B is an 8 percent continuously compounded lump sum investment, also good for 15 years. How much money would you need to invest in B today for it to be worth as much as investment A 15 years from now?
A local finance company quotes a 16 percent interest rate on one-year loans. So, if you borrow $25,000 the interest for the year will be $4,000. Because you must repay a total of $29,000 in one year, the finance company requires you to pay $29,000/12, or $2,416.67, per month over the next 12 months. Is this a 16 percent loan? What rate would legally have to be quoted? What is the effective annual rate?
3. In order to find the amount to invest in B, we first need to know the future value of investment A since that is the amount that investment B should grow to in 15 years.
Investment A is an annuity and so we need to calculate the FV of annuity. The time period is 15 X 12 = 180 months, interest rate is 8.5%/12 = 0.71% and ...
What is the effective annual rate?
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