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- Louis is saving for his retirement by making annual end of year deposits for 30 years into a bank account that pays interest at a nominal rate of 8% compounded quarterly. For the first 10 years the deposits are level at $5000 each year. After the 10 th year, each deposit is 3% more than the year before. A) Give an actuarial expression for the account balance after the final deposit is made ? B) What is the account balance after the final deposit is made ?You invest $3,000 in a Certificate of Deposit paying an annual compound interest of 1.26% for 10 years and then move it into a savings account that pays 0.70% interest compounded annually. What is the final balance in your account at the end of 18 years?You deposit $1,500 at the end of the year (k = 0) into an account that pays interest at a rate of 7% compounded annually. A year after your deposit, the savings account interest rate changes to 12% nominal interest compounded monthly. Six years after your deposit, the savings account again changes its interest rate; this time the interest rate becomes 8% nominal interest compounded quarterly. Eight years after your deposit, the saving account changes its rate once more to 6% compounded annually. a. How much money should be in the savings account 18 years after the initial deposit, assuming no further changes in the account's interest rate? b. What interest rate, compounded annually, is equivalent to the interest pattern of the saving account in Part (a) over the entire 18 year period? a. $ should be in the savings account 18years after the initial deposit. (Round to the nearest dollar.) b. The interest rate equivalent to the interest pattern of the saving account in Part (a) over the…
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- A regular deposit of $120 is made at the beginning of each year for 20 years. Simple interest is calculatedat a rate of i per year for 22 years. At the end of the 22-year period, the total amount in the account is $9600.Suppose that interest at the same rate i compounded annually had been paid instead. How much interest wouldhave been in the account at the end of the 22 years?You deposit $1.2 milion into vour account to cover expenses in the next 12 vears. The account earns interest at the rate of 4%, compounded annually. Assume you expect the balance of the account to be $0 at the end of the 12th year. A) What annual level of living expenses Will your initial deposit support. (e.g., what equal annual withdrawal can you make for the next 12 years )? b) Suppose you realize your living expenses will increase at an annual rate of 2% due to inflation. Determine the updated annual spending plan in the line with this model how much can you withdrawal at the end of the first year. knowing that your withdrawal will increase by 2% each year? C) Suppose the initial deposit is still planned to support your equal annual expenses in the next 10 years as in part a but don't need to withdraw any money from your account for the first 6 years. You will withdraw from your account annually starting from the end of year 7 till the end of year 12. What annual level of living…You deposit $1,000 at the end of the year (k = 0) into an account that pays interest at a rate of 6% compounded annually. Two years after your deposit, the savings account interest rate changes to 12% nominal interest compounded monthly. Six years after your deposit, the savings account again changes its interest rate; this time the interest rate becomes 8% nominal interest compounded quarterly. Nine years after your deposit, the saving account changes its rate once more to 5% compounded annually. a. How much money should be in the savings account 18 years after the initial deposit, assuming no further changes in the account's interest rate? b. What interest rate, compounded annually, is equivalent to the interest pattern of the saving account in Part (a) over the entire 18 year period? a. S should be in the savings account 18 years after the initial deposit. (Round to the nearest dollar.) b. The interest rate equivalent to the interest pattern of the saving account in Part (a) over…
