Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $7840

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 = $7840 – $4900 = $2940

Thus, Simple Interest = $2940

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 × 2940}/_{4900 × 6}

= ²⁹⁴⁰⁰⁰/₂₉₄₀₀

= 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) = $4900

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

Simple Interest = $2940 (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 $4900

= ⁶/₁₀₀ × 4900

= ^{6 × 4900}/₁₀₀

= ²⁹⁴⁰⁰/₁₀₀ = 294

Thus, simple Interest for 1 year = $294

Now,

∵ If the simple Interest is $294, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₉₄ years

∴ If the simple Interest is $2940, then the time = ¹/₂₉₄ × 2940 years

= ^{1 × 2940}/₂₉₄ years

= ²⁹⁴⁰/₂₉₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.

(3) If John borrowed $3200 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.

(5) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?

(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(8) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?