Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4700

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6674

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 = $6674 – $4700 = $1974

Thus, Simple Interest = $1974

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 × 1974}/_{4700 × 6}

= ¹⁹⁷⁴⁰⁰/₂₈₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4700

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1974 (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 = 6% of Principal

= 6% of $4700

= ⁶/₁₀₀ × 4700

= ^{6 × 4700}/₁₀₀

= ²⁸²⁰⁰/₁₀₀ = 282

Thus, simple Interest for 1 year = $282

Now,

∵ If the simple Interest is $282, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₂ years

∴ If the simple Interest is $1974, then the time = ¹/₂₈₂ × 1974 years

= ^{1 × 1974}/₂₈₂ years

= ¹⁹⁷⁴/₂₈₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(2) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(3) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.

(5) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.

(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.