Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 10% 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  9

Solution & Explanation

Solution

Given,

Principal (P) = $6900

Rate of Simple Interest (R) = 10% 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 × 10}

= ⁶²¹⁰⁰⁰/₆₉₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = 10% 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 = 10% of Principal

= 10% of $6900

= ¹⁰/₁₀₀ × 6900

= ^{10 × 6900}/₁₀₀

= ⁶⁹⁰⁰⁰/₁₀₀ = 690

Thus, simple Interest for 1 year = $690

Now,

∵ If the simple Interest is $690, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₉₀ years

∴ If the simple Interest is $6210, then the time = ¹/₆₉₀ × 6210 years

= ^{1 × 6210}/₆₉₀ years

= ⁶²¹⁰/₆₉₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.

(2) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.

(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

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

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.

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

(8) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?

(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?