Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $7040

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7040 – $4400 = $2640

Thus, Simple Interest = $2640

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2640}/_{4400 × 10}

= ²⁶⁴⁰⁰⁰/₄₄₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $4400

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $2640 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 10% of Principal

= 10% of $4400

= ¹⁰/₁₀₀ × 4400

= ^{10 × 4400}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₀ years

∴ If the simple Interest is $2640, then the time = ¹/₄₄₀ × 2640 years

= ^{1 × 2640}/₄₄₀ years

= ²⁶⁴⁰/₄₄₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.

(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

(3) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.

(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?

(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.

(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.