Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $10168

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 = $10168 – $6200 = $3968

Thus, Simple Interest = $3968

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 × 3968}/_{6200 × 8}

= ³⁹⁶⁸⁰⁰/₄₉₆₀₀

= 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) = $6200

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

Simple Interest = $3968 (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 $6200

= ⁸/₁₀₀ × 6200

= ^{8 × 6200}/₁₀₀

= ⁴⁹⁶⁰⁰/₁₀₀ = 496

Thus, simple Interest for 1 year = $496

Now,

∵ If the simple Interest is $496, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₆ years

∴ If the simple Interest is $3968, then the time = ¹/₄₉₆ × 3968 years

= ^{1 × 3968}/₄₉₆ years

= ³⁹⁶⁸/₄₉₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?

(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.

(5) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.

(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?