Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7480

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 = $7480 – $4400 = $3080

Thus, Simple Interest = $3080

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 × 3080}/_{4400 × 7}

= ³⁰⁸⁰⁰⁰/₃₀₈₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 7% per annum

Simple Interest = $3080 (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 = 7% of Principal

= 7% of $4400

= ⁷/₁₀₀ × 4400

= ^{7 × 4400}/₁₀₀

= ³⁰⁸⁰⁰/₁₀₀ = 308

Thus, simple Interest for 1 year = $308

Now,

∵ If the simple Interest is $308, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₈ years

∴ If the simple Interest is $3080, then the time = ¹/₃₀₈ × 3080 years

= ^{1 × 3080}/₃₀₈ years

= ³⁰⁸⁰/₃₀₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?

(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.

(5) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(6) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(9) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.