Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5200

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

Amount (A) = $7696

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 = $7696 – $5200 = $2496

Thus, Simple Interest = $2496

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 × 2496}/_{5200 × 6}

= ²⁴⁹⁶⁰⁰/₃₁₂₀₀

= 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) = $5200

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

Simple Interest = $2496 (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 $5200

= ⁶/₁₀₀ × 5200

= ^{6 × 5200}/₁₀₀

= ³¹²⁰⁰/₁₀₀ = 312

Thus, simple Interest for 1 year = $312

Now,

∵ If the simple Interest is $312, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₂ years

∴ If the simple Interest is $2496, then the time = ¹/₃₁₂ × 2496 years

= ^{1 × 2496}/₃₁₂ years

= ²⁴⁹⁶/₃₁₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(2) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.

(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.

(7) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?

(8) If Betty paid $5100 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 Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.