Simple Interest
Math MCQs

Question :    How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?

Correct Answer  $6350

Solution & Explanation

Solution

Given,

Amount (A) = $7620

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

$7620 = P (1 + 4% × 5)

⇒ $7620 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7620 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7620 = P (1 + ²⁰/₁₀₀)

⇒ $7620 = P (^{100 + 20}/₁₀₀)

⇒ $7620 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7620

⇒ P = ⁷⁶²⁰/_¹²⁰/100

⇒ P = 7620 × ¹⁰⁰/₁₂₀

⇒ P = ^{7620 × 100}/₁₂₀

⇒ P = ⁷⁶²⁰⁰⁰/₁₂₀

⇒ P = $6350

Thus, the sum borrowed (P) = $6350 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 7620, then the Principal = ¹⁰⁰/₁₂₀ × 7620

= ^{100 × 7620}/₁₂₀

= ⁷⁶²⁰⁰⁰/₁₂₀

= 6350

Thus, Principal = $6350

Thus, the sum borrowed = $6350 Answer

Similar Questions

(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.

(4) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.

(5) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(7) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(9) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.