Simple Interest
Math MCQs

Question :    How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

Correct Answer  $7750

Solution & Explanation

Solution

Given,

Amount (A) = $9300

Rate of Simple Interest (R) = 4%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$9300 = P (1 + 4% × 5)

⇒ $9300 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9300 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9300 = P (1 + ²⁰/₁₀₀)

⇒ $9300 = P (^{100 + 20}/₁₀₀)

⇒ $9300 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9300

⇒ P = ⁹³⁰⁰/_¹²⁰/100

⇒ P = 9300 × ¹⁰⁰/₁₂₀

⇒ P = ^{9300 × 100}/₁₂₀

⇒ P = ⁹³⁰⁰⁰⁰/₁₂₀

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 9300, then the Principal = ¹⁰⁰/₁₂₀ × 9300

= ^{100 × 9300}/₁₂₀

= ⁹³⁰⁰⁰⁰/₁₂₀

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer

Similar Questions

(1) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?

(2) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.

(8) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.

(10) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.