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) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(3) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.

(4) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(5) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?

(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.

(9) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?

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