Simple Interest
Math MCQs

Question :    How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

Correct Answer  $7250

Solution & Explanation

Solution

Given,

Amount (A) = $8700

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

$8700 = P (1 + 4% × 5)

⇒ $8700 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8700 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8700 = P (1 + ²⁰/₁₀₀)

⇒ $8700 = P (^{100 + 20}/₁₀₀)

⇒ $8700 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8700

⇒ P = ⁸⁷⁰⁰/_¹²⁰/100

⇒ P = 8700 × ¹⁰⁰/₁₂₀

⇒ P = ^{8700 × 100}/₁₂₀

⇒ P = ⁸⁷⁰⁰⁰⁰/₁₂₀

⇒ P = $7250

Thus, the sum borrowed (P) = $7250 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 8700, then the Principal = ¹⁰⁰/₁₂₀ × 8700

= ^{100 × 8700}/₁₂₀

= ⁸⁷⁰⁰⁰⁰/₁₂₀

= 7250

Thus, Principal = $7250

Thus, the sum borrowed = $7250 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

(3) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(4) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?

(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(7) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.

(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.