Simple Interest
Math MCQs

Question :    How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?

Correct Answer  $7700

Solution & Explanation

Solution

Given,

Amount (A) = $9625

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

$9625 = P (1 + 5% × 5)

⇒ $9625 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9625 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9625 = P (1 + ²⁵/₁₀₀)

⇒ $9625 = P (^{100 + 25}/₁₀₀)

⇒ $9625 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9625

⇒ P = ⁹⁶²⁵/_¹²⁵/100

⇒ P = 9625 × ¹⁰⁰/₁₂₅

⇒ P = ^{9625 × 100}/₁₂₅

⇒ P = ⁹⁶²⁵⁰⁰/₁₂₅

⇒ P = $7700

Thus, the sum borrowed (P) = $7700 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 9625, then the Principal = ¹⁰⁰/₁₂₅ × 9625

= ^{100 × 9625}/₁₂₅

= ⁹⁶²⁵⁰⁰/₁₂₅

= 7700

Thus, Principal = $7700

Thus, the sum borrowed = $7700 Answer

Similar Questions

(1) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(3) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?

(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?

(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(8) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.

(10) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.