Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $7252

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 = $7252 – $4900 = $2352

Thus, Simple Interest = $2352

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 × 2352}/_{4900 × 6}

= ²³⁵²⁰⁰/₂₉₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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 = $2352 (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 $2352, then the time = ¹/₂₉₄ × 2352 years

= ^{1 × 2352}/₂₉₄ years

= ²³⁵²/₂₉₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?

(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.

(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(6) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(9) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.