Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $11247

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 = $11247 – $6900 = $4347

Thus, Simple Interest = $4347

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 × 4347}/_{6900 × 7}

= ⁴³⁴⁷⁰⁰/₄₈₃₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $6900

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

Simple Interest = $4347 (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 $6900

= ⁷/₁₀₀ × 6900

= ^{7 × 6900}/₁₀₀

= ⁴⁸³⁰⁰/₁₀₀ = 483

Thus, simple Interest for 1 year = $483

Now,

∵ If the simple Interest is $483, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₃ years

∴ If the simple Interest is $4347, then the time = ¹/₄₈₃ × 4347 years

= ^{1 × 4347}/₄₈₃ years

= ⁴³⁴⁷/₄₈₃ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?

(2) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.

(3) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

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

(7) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(8) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.

(10) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.