Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 10% 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  6

Solution & Explanation

Solution

Given,

Principal (P) = $4900

Rate of Simple Interest (R) = 10% 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 × 10}

= ²⁹⁴⁰⁰⁰/₄₉₀₀₀

= 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) = $4900

Rate of Simple Interest (R) = 10% 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 = 10% of Principal

= 10% of $4900

= ¹⁰/₁₀₀ × 4900

= ^{10 × 4900}/₁₀₀

= ⁴⁹⁰⁰⁰/₁₀₀ = 490

Thus, simple Interest for 1 year = $490

Now,

∵ If the simple Interest is $490, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₀ years

∴ If the simple Interest is $2940, then the time = ¹/₄₉₀ × 2940 years

= ^{1 × 2940}/₄₉₀ years

= ²⁹⁴⁰/₄₉₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.

(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(7) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(8) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?

(9) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.