Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5100

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

Amount (A) = $8160

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 = $8160 – $5100 = $3060

Thus, Simple Interest = $3060

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 × 3060}/_{5100 × 6}

= ³⁰⁶⁰⁰⁰/₃₀₆₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5100

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

Simple Interest = $3060 (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 $5100

= ⁶/₁₀₀ × 5100

= ^{6 × 5100}/₁₀₀

= ³⁰⁶⁰⁰/₁₀₀ = 306

Thus, simple Interest for 1 year = $306

Now,

∵ If the simple Interest is $306, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₆ years

∴ If the simple Interest is $3060, then the time = ¹/₃₀₆ × 3060 years

= ^{1 × 3060}/₃₀₆ years

= ³⁰⁶⁰/₃₀₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.

(5) Kenneth had to pay $5450 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 Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?

(8) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.

(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(10) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.