Geometric progression - practice problems - page 6 of 14

Number of problems found: 280

The town
The town population is 56000. It is decreasing by 2% every year. What will be the population of the town after 13 years?
Saving for education
Suppose a couple invested ₱50,000 in an account when their child was born, to save for college. The average annual interest rate is 4.4%, compounded annually. a) Give an exponential model for the situation. b) Will the money have doubled by the time the c
Sequences AP + GP
The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, the second 4, and keep the third, we get the geometric series. Find AP and GP members.
Annual interest
A loan of 10 000 euros is to be repaid in annual payments over ten years. Assuming a fixed 10% annual interest rate compounded annually, calculate: (a) the amount of each annual repayment (b) the total interest paid.
Interest rate
We borrowed CZK 50,000. The annual interest rate was 6%. We have to repay the entire debt in 5 years. How much will we pay? (use the compound interest relationship).
Loan debt
We borrowed CZK 150,000 at a monthly interest rate of 2%. Interest is added at the end of each month, and we immediately pay an installment of CZK 30,000. How much will we owe in five months?
Bank withdrawal time
We will deposit € 10,500 at the bank at 1.1% interest, and we want to withdraw € 11,000. How many years do we have to wait? Round to 2 decimal places.
Population growth percentage
The population increased from 29,000 to 31,500 in 5 years. Calculate the average annual population growth in percents.
Annual growth
The population has grown from 25,000 to 33,600 in 10 years. Calculate what the average annual population growth in% was.
Machine depreciation
The initial price of the machine is 23,000 euros. Every year, 12% of its cost is depreciated due to wear and tear. What value will the machine have after six years?
Bank withdrawal time
We will deposit € 8,500 into the bank at 1.3% interest and withdraw € 8,700. How many years do we have to wait? Round to 2 decimal places.
Annual increase
The number of cars produced increased from 45,000 to 47,000 in 3 years. Calculate the average annual increase in cars in%.
House increase percentage
On the pages of the Czech Statistical Office, we can learn that in 1869, Prague and its suburbs had a total of 10,947 houses; in 1900, there were 18,838 houses. What was the annual percentage "increase" of houses in Prague between 1869 and 1900, assuming
Forest wood growth
The amount of wood in a specific forest area is estimated at 2,106 m³, and the annual wood growth is 2.1%. What will be the situation after 20 years?
Wire diameter reduction
With a single pull, the wire diameter is reduced by 10%. How many draws are required to minimize the wire diameter from 5 mm to less than half?
Six terms GP
Find the sum of the six terms of the finite geometric sequence 96, -48, 24, -12
Consecutive members
The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, and c of the blocks for which a < b < c and a + b + c = 38 cm and whose numerical values in cm represent three consecutive members of the geometric sequence.
Present value
A bank loans a family $90,000 at a 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making monthly payments over 15 years. How much should the monthly payment be in order to pay off the debt in 15 years?
Savings
Suppose on your 21st birthday, you begin making monthly payments of $500 into an account that pays 8% compounded monthly. If you continue the payments until your 51st birthday (30 years), How much money is in your account? How much of it is interesting? S
Future value
Suppose you invested $1000 per quarter over 15 years. If money earns an annual rate of 6.5% compounded quarterly, how much would be available at the end of the time period? How much is the interest earned?

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