Math Problem Statement
Solution
To solve the given problems, let's break down each section:
(a) Find the interest rate per annum.
Mandy deposited $100,000 in bank A with simple interest and obtained $12,000 after 3 years.
- Simple Interest Formula:
where:- is the principal amount ($100,000),
- is the rate of interest per annum,
- is the time in years (3 years).
Given:
Thus, the interest rate is 4% per annum.
(b) Find the total interest that Mandy earned at the end of 2023, correct to the nearest dollar.
The deposit was moved to bank B on January 1, 2023, where it is compounded quarterly with the same interest rate (4% per annum).
- Compounded Interest Formula:
where:- is the amount after interest,
- is the number of compounding periods per year (4 for quarterly),
- is the number of years (1 year for 2023).
Substitute the values:
Interest earned = Amount - Principal
Thus, the total interest earned is $4,547.
(c) Find the minimum value of if Mandy would like to have more than $200,000 in her account at the end of 2025.
Calculate the future value of the $116,547 (from 2023 end to 2025 end).
For 2 years compounded quarterly at 4% per annum:
To achieve more than $200,000:
Thus, the minimum value of is $68,865 (rounded to the nearest integer).
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Simple Interest
Compound Interest
Exponential Growth
Formulas
Simple Interest Formula: SI = P × r × t
Compound Interest Formula: A = P(1 + r/n)^(n × t)
Theorems
-
Suitable Grade Level
Grades 10-12
Related Recommendation
Monthly Deposit and Interest Calculation for $400,000 Retirement in 20 Years at 8% Interest
Simple and Compound Interest Calculations: 5.5% and 6% Over Five Years
Simple and Compound Interest Calculations for $4000 and $2000 Investments
Quarterly Deposits to Save $22,000 Over 6 Years with 4.9% Interest
Compound Interest Problem: Initial Deposit for 4.2% Interest Over 6.75 Years