Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $6068

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 = $6068 – $4100 = $1968

Thus, Simple Interest = $1968

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 × 1968}/_{4100 × 6}

= ¹⁹⁶⁸⁰⁰/₂₄₆₀₀

= 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) = $4100

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

Simple Interest = $1968 (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 $4100

= ⁶/₁₀₀ × 4100

= ^{6 × 4100}/₁₀₀

= ²⁴⁶⁰⁰/₁₀₀ = 246

Thus, simple Interest for 1 year = $246

Now,

∵ If the simple Interest is $246, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₄₆ years

∴ If the simple Interest is $1968, then the time = ¹/₂₄₆ × 1968 years

= ^{1 × 1968}/₂₄₆ years

= ¹⁹⁶⁸/₂₄₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(3) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.

(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.

(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.