Simple Interest
MCQs Math

Question:     Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $6560

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 = $6560 – $4100 = $2460

Thus, Simple Interest = $2460

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 × 2460}/_{4100 × 6}

= ²⁴⁶⁰⁰⁰/₂₄₆₀₀

= 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) = $4100

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

Simple Interest = $2460 (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 $4100

= ⁶/₁₀₀ × 4100

= ^{6 × 4100}/₁₀₀

= ²⁴⁶⁰⁰/₁₀₀ = 246

Thus, simple Interest for 1 year = $246

Now,

∵ If the simple Interest is $246, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₄₆ years

∴ If the simple Interest is $2460, then the time = ¹/₂₄₆ × 2460 years

= ^{1 × 2460}/₂₄₆ years

= ²⁴⁶⁰/₂₄₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.

(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.

(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(8) 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.

(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.

(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.