Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 8% 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  6

Solution & Explanation

Solution

Given,

Principal (P) = $4900

Rate of Simple Interest (R) = 8% 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 × 8}

= ²³⁵²⁰⁰/₃₉₂₀₀

= 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) = 8% 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 = 8% of Principal

= 8% of $4900

= ⁸/₁₀₀ × 4900

= ^{8 × 4900}/₁₀₀

= ³⁹²⁰⁰/₁₀₀ = 392

Thus, simple Interest for 1 year = $392

Now,

∵ If the simple Interest is $392, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₂ years

∴ If the simple Interest is $2352, then the time = ¹/₃₉₂ × 2352 years

= ^{1 × 2352}/₃₉₂ years

= ²³⁵²/₃₉₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(4) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(5) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(6) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?

(8) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.

(9) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.