# solve the questions with maths

1.Johnson is saving up to buy a piano in three years. In three years, the piano will cost 5000. To save up to purchase the piano, Johnson makes level end of month deposits in to a savings account crediting interest at a nominal rate of 12% convertible monthly. In what amount are Johnsonâ€™s monthly deposits?

2.Albert and Allison borrow exactly the same amount from Liberty Financial. Albert will repay his loan with 20 end of year annual payments. Albertâ€™s first payment will be 1000, and each of his successive payments will be 1000 greater than the one before. Allison will make level payments of 50000 at times T,2T,3T,4T. Both Albert and Allisonâ€™s loans are subject to the same annual effective rate of 5%. Determine the time of Allisonâ€™s first payment.

3.Charities A, B and C split level payments of X at the end of each year forever. For the first n years, two-thirds of the payment will be given to Charity A and the other one-third of the payment to Charity B. Thereafter, all payments will be directed to Charity C. If the annual effective interest rate for the perpetuity is 10%, then the proportion of the present value going to Charity C is 0.385 543 289 4. If the present value of the inheritance is based on an annual effective interest rate of 8%, then what is the proportion of the present value going to Charity B?

4.Jim is leasing a new car. The price of the car is 35,000. The terms of the lease go as follows. There are 120 monthly payments with the first payment being one month from now. The nominal rate of interest is 8.4% convertible monthly. The payments in the first year are X. In the second year, the payments are 0.9X, in the third 0.92X and so on. Just after his 60th payment, Jim sells his car for Y dollars. Before Jim receives a check, he first must pay off the outstanding loan balance still owed just after his 60th payment to the lender. What is the smallest value of Y such that Jimâ€™s check is at least 20000?

5. Susan takes out a loan for 80,000. She is to repay the loan with 360 level monthly payments (with the only possible exception of the final payment due to rounding up the payment to the nearest cent) with the first occurring one month from today. The nominal rate of interest is 6% convertible monthly for the first 15 years and 4.8% convertible monthly for the next 15 years. What is the amount of interest paid in the first 180 monthly payments? (Round up the first 359 payments to the nearest cent.)

6.Ken planned to make monthly deposits in to a saving account at a nominal rate of 3% compounded monthly for 180 months. The amount of deposit is k at the end of the k th month, where k = 1, 2, …, 180. However, he was unemployed for a short period of time, so he missed the 1st through 10th payments. He made the rest of the payments as planned. How much does Ken have in his saving account at the end of the 180th month after the last deposit?

7.If a inf i = 20, then what is a(two dots) inf 2i? (Round your answer to the nearest integer.)

8.John and Susan purchased a house in NY state five years ago. The purchasing price of the house was $600,000. The couple made a down payment of$125,000, and they were approved for a 30-year mortgage. The terms of the mortgage are as follows. There are 360 level monthly payments, with the exception of the final payment being slightly reduced. The nominal interest rate is 3% convertible monthly. They recently sold the house for $650,000 immediately after the 60th mortgage payment. They also need to pay 6% of the selling price to the real estate agents. How much cash can they receive after paying mortgage balance and real estate agent commission, assuming there is no other cost?

9. A twenty-year annuity is purchased at a 3% annual effective interest rate. The first payment of the annuity is due in five years in the amount of 2000. The subsequent payments decrease by 100 each year. What is the price of the annuity at the time of purchase? (Round your answer to the nearest integer.)

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