Simple Interest
Math MCQs

Question :    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.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $12060

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 = $12060 – $6700 = $5360

Thus, Simple Interest = $5360

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 × 5360}/_{6700 × 8}

= ⁵³⁶⁰⁰⁰/₅₃₆₀₀

= 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) = $6700

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $5360 (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 $6700

= ⁸/₁₀₀ × 6700

= ^{8 × 6700}/₁₀₀

= ⁵³⁶⁰⁰/₁₀₀ = 536

Thus, simple Interest for 1 year = $536

Now,

∵ If the simple Interest is $536, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₆ years

∴ If the simple Interest is $5360, then the time = ¹/₅₃₆ × 5360 years

= ^{1 × 5360}/₅₃₆ years

= ⁵³⁶⁰/₅₃₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

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

(2) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(3) 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.

(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.

(7) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.

(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.