Simple Interest
Math MCQs

Question :    How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $6250

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

$6250 = P (1 + 5% × 5)

⇒ $6250 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6250 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6250 = P (1 + ²⁵/₁₀₀)

⇒ $6250 = P (^{100 + 25}/₁₀₀)

⇒ $6250 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6250

⇒ P = ⁶²⁵⁰/_¹²⁵/100

⇒ P = 6250 × ¹⁰⁰/₁₂₅

⇒ P = ^{6250 × 100}/₁₂₅

⇒ P = ⁶²⁵⁰⁰⁰/₁₂₅

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 6250, then the Principal = ¹⁰⁰/₁₂₅ × 6250

= ^{100 × 6250}/₁₂₅

= ⁶²⁵⁰⁰⁰/₁₂₅

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.

(3) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?

(5) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.

(7) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.

(9) 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.

(10) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.