Simple Interest
Math MCQs

Question :    How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?

Correct Answer  $5200

Solution & Explanation

Solution

Given,

Amount (A) = $6500

Rate of Simple Interest (R) = 5%

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

$6500 = P (1 + 5% × 5)

⇒ $6500 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6500 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6500 = P (1 + ²⁵/₁₀₀)

⇒ $6500 = P (^{100 + 25}/₁₀₀)

⇒ $6500 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6500

⇒ P = ⁶⁵⁰⁰/_¹²⁵/100

⇒ P = 6500 × ¹⁰⁰/₁₂₅

⇒ P = ^{6500 × 100}/₁₂₅

⇒ P = ⁶⁵⁰⁰⁰⁰/₁₂₅

⇒ P = $5200

Thus, the sum borrowed (P) = $5200 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6500, then the Principal = ¹⁰⁰/₁₂₅ × 6500

= ^{100 × 6500}/₁₂₅

= ⁶⁵⁰⁰⁰⁰/₁₂₅

= 5200

Thus, Principal = $5200

Thus, the sum borrowed = $5200 Answer

Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?

(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.

(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

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

(7) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?