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) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.

(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.

(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?

(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?

(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.

(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.