Eric deposits X into a savings account at time 0, which pays interest at a nominal rate of compounded semi-annually. Mike deposits into a different savings account at time 0, which pays simple interest at an annual rate of : Eric and Mike earn the same amount of interest during the last 6 months of the 8th year. Calculate .

1. I pay 250,000 into an account today. The account pays simple interest at a rate of 5% pa. How much will I have in my account in 7 year’s time?
2. When calculate: ( ) b. ( ) c. ( ) d. ( )
3. Given that ( ) and ( ) Find
4. Suppose that you invest $4,000 at time 0 into an investment account with an accumulation function of ( ) . At time 4, your investment has accumulated to $5,000. Find the accumulated value of your investment at time 10.
5. Eric deposits X into a savings account at time 0, which pays interest at a nominal rate of compounded semi-annually. Mike deposits into a different savings account at time 0, which pays simple interest at an annual rate of : Eric and Mike earn the same amount of interest during the last 6 months of the 8th year. Calculate .
6. Bruce deposits 100 into a bank account. His account is credited interest at a nominal rate of interest of 4% convertible semi-annually. At the same time, Peter deposits 100 into a separate account. Peter”s account is credited interest at a force of interest of . After 7.25 years, the value of each account is the same. Calculate .
7. At a certain rate of simple interest, 1,000 will accumulate to 1,100 after a certain period of time. Find the accumulated value of 500 at a rate of simple interest three fourths as great over twice the as long a period of time.
8. Fund A is invested at an effective interest rate of 3%. Fund B is invested at an effective interest rate of 2.5%. At the end of 20 years, the total in the two funds is 10,000. At the end of 31 years the amount in fund A is twice the amount in fund B. Calculate the total in the two funds at the end of ten years.
9. It can be shown that for an interest rate, , where :
? ( ) for
? ( ) for
? ( ) for
Discuss and then represent this theorem graphically.
10. Show that: ( ) ( )

 

 

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