Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6900

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $13110

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 = $13110 – $6900 = $6210

Thus, Simple Interest = $6210

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 × 6210}/_{6900 × 9}

= ⁶²¹⁰⁰⁰/₆₂₁₀₀

= 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) = $6900

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $6210 (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 = 9% of Principal

= 9% of $6900

= ⁹/₁₀₀ × 6900

= ^{9 × 6900}/₁₀₀

= ⁶²¹⁰⁰/₁₀₀ = 621

Thus, simple Interest for 1 year = $621

Now,

∵ If the simple Interest is $621, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂₁ years

∴ If the simple Interest is $6210, then the time = ¹/₆₂₁ × 6210 years

= ^{1 × 6210}/₆₂₁ years

= ⁶²¹⁰/₆₂₁ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.

(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(4) 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.

(5) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.

(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?

(9) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(10) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.