Mr. Wang has a principal of 1000 yuan, invested for 5 years, and set up a bank with compound interest rate of 8%, compounded once a quarter. What is the interest due and what is the actual interest rate

Mr. Wang has a principal of 1000 yuan, invested for 5 years, and set up a bank with compound interest rate of 8%, compounded once a quarter. What is the interest due and what is the actual interest rate

Compound interest once a quarter, the quarterly interest rate is 8% / 4 = 2%, compound interest 5 * 4 = 20 times
Maturity interest = 1000 * (1 + 2%) ^ 20-1000 = 485.95 yuan

If we want the final value of compound interest to be 3 times of the principal after 8 years and compound interest once a quarter, what is the annual interest rate?

There are 4 * 8 = 32 interest periods in 8 years, that is, (1 + I) ^ 32 = 3
I = 0.0349 = 0.35
Then the annual interest rate = 4 * 0.35 = 14%

At the beginning of each year, I raised 1000 yuan from the bank for 10 years, with an annual interest rate of 9%. Now how much money do I need to deposit with the bank at one time
Notice the beginning of the year

This is to calculate the present value of an immediate annuity. The coefficient of the present value of an immediate annuity = (1 - (1 + 9%) ^ (- 10)) / (9% * (1 + 9%)) = 5.887759
Therefore, the amount of one-time deposit in the bank is 1000 * 5.887759 = 58877.59 yuan