Maths of Interest

1. You are given (i) Fund A accumulates at an interest rate of 12% compounded monthly. (ii) Fund B accumulates at an interest rate of 6% compounded semiannually. (iii) At the end of 10 year, the total amount in the two finds combined is 2000. (iv) At the end of 5 years, the amount in Fund A is twice that in Fund B . Calculate the total amount in the two funds at the end of 2 years. 2. Nicholas borrow 2,000 from Kavitha at an annual effective rate of interest,i . He agrees to pay back 2,000 after eight years and 1,410.84 after another eight years. Four years after his 1st payment, Nicholas repays the outstanding balance. What is the amount of Nicholas’s second payment? 3. Kelly deposits 1000 into a fund which credits interest at a nominal interest rate of 10% compounded semiannually. At the same time, he deposits P into a different fund which credits interest at a nominal discount rate of 6% compounded monthly. 20 years later, the amount in each fund is equal. Find P . 4. You are given: (i) 1/ /(2 ) t δ = + t ; and (ii) The total interest earned during the first n years on an investment of 1 at time t = 0 is 15. Determine n . 5. A person age 40 wishes to accumulate a fund for retirement by depositing an amount X at the end of each year into an account paying 4% interest. At age 65, the person will use the entire account balance to purchase a 15-year 5% annuity-immediate with annual payments of $10,000. Find X . 6. Michele wants to purchase a perpetuity paying 100 per year with the first payment due at the end of year 11. He can purchase it by either: (i) Paying 90 per year at the end of each year for 10 years; or (ii) Paying K per year at the end of each year for the first 5 years and nothing for the next 5 years. Calculate K . 7. Daniel and Cheryl are planning to retire on January 1, 2035. Their goal is to have enough money in savings to be able to withdraw $3,000 per month beginning one month after retirement and continuing for 25 years after retirement. They earn an annual effective rate of interest of 10% on their account. Determine the minimum amount needed in their savings account on January 1, 2035, to accomplish their goal. 8. You deposit 10,000 into a bank for seven years at an annual effective interest rate of 5%. At the end of seven years, you make 120 equal month withdrawal of X with the first withdrawal made immediately. During the withdrawal period, interest is credited at an annual effective interest rate of 3%. Calculate X .