Simple Interest
Math MCQs

Question :    How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

Correct Answer  $5700

Solution & Explanation

Solution

Given,

Amount (A) = $6840

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

$6840 = P (1 + 4% × 5)

⇒ $6840 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6840 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6840 = P (1 + ²⁰/₁₀₀)

⇒ $6840 = P (^{100 + 20}/₁₀₀)

⇒ $6840 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6840

⇒ P = ⁶⁸⁴⁰/_¹²⁰/100

⇒ P = 6840 × ¹⁰⁰/₁₂₀

⇒ P = ^{6840 × 100}/₁₂₀

⇒ P = ⁶⁸⁴⁰⁰⁰/₁₂₀

⇒ P = $5700

Thus, the sum borrowed (P) = $5700 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 6840, then the Principal = ¹⁰⁰/₁₂₀ × 6840

= ^{100 × 6840}/₁₂₀

= ⁶⁸⁴⁰⁰⁰/₁₂₀

= 5700

Thus, Principal = $5700

Thus, the sum borrowed = $5700 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(2) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.

(4) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

(5) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(7) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?