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) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(4) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?

(5) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(8) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.