Simple Interest
Math MCQs

Question :    How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?

Correct Answer  $5800

Solution & Explanation

Solution

Given,

Amount (A) = $6670

Rate of Simple Interest (R) = 3%

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

$6670 = P (1 + 3% × 5)

⇒ $6670 = P (1 + ³/₁₀₀ × 5)

⇒ $6670 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6670 = P (1 + ¹⁵/₁₀₀)

⇒ $6670 = P (^{100 + 15}/₁₀₀)

⇒ $6670 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6670

⇒ P = ⁶⁶⁷⁰/_¹¹⁵/100

⇒ P = 6670 × ¹⁰⁰/₁₁₅

⇒ P = ^{6670 × 100}/₁₁₅

⇒ P = ⁶⁶⁷⁰⁰⁰/₁₁₅

⇒ P = $5800

Thus, the sum borrowed (P) = $5800 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6670, then the Principal = ¹⁰⁰/₁₁₅ × 6670

= ^{100 × 6670}/₁₁₅

= ⁶⁶⁷⁰⁰⁰/₁₁₅

= 5800

Thus, Principal = $5800

Thus, the sum borrowed = $5800 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(2) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(5) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.

(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?

(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.

(9) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.