Asked by Daniel Carrera Chavarria on May 30, 2024
Verified
An investment earning 16% simple interest has a maturity value of $9,440.00 after eight months. What was the initial amount invested?
A) $8,530.12
B) $10,446.93
C) $7,228.92
D) $8,853.33
E) $7,780.22
Simple Interest
Interest figured solely on the initial sum, excluding any compounded amounts.
Maturity Value
The amount that will be received at the end of a fixed-term investment, including the principal and any accumulated interest.
Initial Amount
The starting amount of money before any growth or shrinkage due to interest or losses.
- Obtain an insight into the conception and computing of simple interest.
- Evaluate the matured value of investments based on simple interest calculations.
Verified Answer
MM
Marian ManteJun 03, 2024
Final Answer :
A
Explanation :
The maturity value of an investment is calculated as the sum of the principal (the initial amount invested) and the interest earned. The formula for simple interest is I=P×r×tI = P \times r \times tI=P×r×t , where III is the interest, PPP is the principal, rrr is the annual interest rate, and ttt is the time in years. Given a 16% annual interest rate and a time of 8 months (which is 812\frac{8}{12}128 or 23\frac{2}{3}32 of a year), we can set up the equation for the maturity value ( MMM ) as M=P+I=P+(P×0.16×23)M = P + I = P + (P \times 0.16 \times \frac{2}{3})M=P+I=P+(P×0.16×32) . Given that the maturity value is $9,440, we can solve for PPP to find the initial investment. Rearranging and solving the equation gives us P=$8,530.12P = \$8,530.12P=$8,530.12 .
Learning Objectives
- Obtain an insight into the conception and computing of simple interest.
- Evaluate the matured value of investments based on simple interest calculations.