Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $6152.5

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

$6152.5 = P (1 + 3% × 5)

⇒ $6152.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6152.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6152.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6152.5 = P (^{100 + 15}/₁₀₀)

⇒ $6152.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6152.5

⇒ P = ^6152.5/_¹¹⁵/100

⇒ P = 6152.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6152.5 × 100}/₁₁₅

⇒ P = ⁶¹⁵²⁵⁰/₁₁₅

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 6152.5, then the Principal = ¹⁰⁰/₁₁₅ × 6152.5

= ^{100 × 6152.5}/₁₁₅

= ⁶¹⁵²⁵⁰/₁₁₅

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?

(3) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?

(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.

(9) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(10) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.