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 $6392 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $6392

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 = $6392 – $4700 = $1692

Thus, Simple Interest = $1692

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 × 1692}/_{4700 × 6}

= ¹⁶⁹²⁰⁰/₂₈₂₀₀

= 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) = $4700

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

Simple Interest = $1692 (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 $1692, then the time = ¹/₂₈₂ × 1692 years

= ^{1 × 1692}/₂₈₂ years

= ¹⁶⁹²/₂₈₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?

(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?

(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.

(5) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?

(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.

(10) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.