Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $7301

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 = $7301 – $4900 = $2401

Thus, Simple Interest = $2401

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 × 2401}/_{4900 × 7}

= ²⁴⁰¹⁰⁰/₃₄₃₀₀

= 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) = $4900

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

Simple Interest = $2401 (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 $4900

= ⁷/₁₀₀ × 4900

= ^{7 × 4900}/₁₀₀

= ³⁴³⁰⁰/₁₀₀ = 343

Thus, simple Interest for 1 year = $343

Now,

∵ If the simple Interest is $343, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₃ years

∴ If the simple Interest is $2401, then the time = ¹/₃₄₃ × 2401 years

= ^{1 × 2401}/₃₄₃ years

= ²⁴⁰¹/₃₄₃ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(2) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?

(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.

(7) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(8) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(9) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(10) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?