Practice IB Mathematics Analysis and Approaches (AA) Topic SL 1.4—financial Apps – Compound Interest, Annual Depreciation with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 1.4—financial Apps – Compound Interest, Annual Depreciation and mirrors Paper 1, 2, 3 style where relevant.
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At the start of July, a colony of bacteria has a population of .
After hours, the population of the bacteria is .
The population of this colony can be calculated using the formula:
where is the population of the bacteria hours after the start of July.
Find and , then calculate the population of the bacteria after hours from the start of July.
Give your answer correct to the nearest integer.
An investor has two options:
Option 1: Invest $ at an annual compound interest rate of . After years, the investment grows to $.
Option 2: Invest $ at an annual compound interest rate of , compounded semi-annually.
Determine the value of , correct to decimal places, such that the value of the investment under Option 2 after years is equal to the value of the investment under Option 1 after years.
A fund receives a single contribution of amount at the end of each year for years. Interest rate is , compounded annually.
Show that the accumulated value after the th deposit is .
If instead is paid at the start of each year (annuity-due), show that the accumulated value after the th payment is .
A target amount (in the same currency as ) must be reached with an annuity-due. Find the least integer required.
A trust fund is established with an initial investment of $10,000. The fund earns compound interest at a rate of per year for the first years. After years, the interest rate changes to per year for the next years.
Calculate the total amount in the trust fund at the end of the -year period. Give your answer correct to the nearest dollar.
Determine the total interest earned over the -year period.
If, at the end of the years, the beneficiary withdraws $5000, and the remaining amount continues to earn compound interest at a rate of per year, how many additional full years will it take for the fund to grow back to at least the amount it held at the end of the initial years?
A company purchases a machine for $25000. The machine depreciates at a rate of per year.
Show that, at the end of 5 years, the machine will be worth approximately $16477, correct to the nearest dollar.
Another company also purchases a machine for $25000. At the end of 3 years, this machine is worth $18000. Find the yearly depreciation rate for this machine.