Simple Interest 2
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Question 1 of 5
1. Question
Robert deposits $$$20{,}000$$ in a bank for `3` years. The interest rate is `7%` per year. What is the amount after `3` years?- `\text(Amount after 3 years)=$` (24200)
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The rate should be expressed as a decimal before it is used in the interest formula.Identify values from the problem.
Principal Value $$= P = $20{,}000$$Interest Rate `= r = 7% \text(per annum) = 0.07 \text((as a decimal))`Time Elapsed `= t = 3` yearsSolve for the Simple Interest Earned`I` `=` `P``r``t` Simple Interest Formula `=` $$$20{,}000$$`xx``0.07``xx``3` Substitute known values `=` $$$4{,}200$$ Solve for the Total AmountTotal Amount `=` $$$20{,}000+$4{,}200$$ `=` $$$24{,}200$$ $$$24{,}200$$ total amount -
Question 2 of 5
2. Question
Carrie deposits $$$2{,}000$$ into a special bank account which earns `$450` at the end of five years. What is the annual interest rate expressed as a percentage?- `\text(Interest Rate )=` (4.5)`%`
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Simple Interest Formula
`I`` = ``P``r``t`Identify the given values
Principal Value $$= P = $2{,}000$$Interest Earned `= $450`Time Elapsed `= t = 5` yearsRewrite the equation to find the interest rate`I` `=` `P``r``t` Simple Interest Formula `r` `=` `I/(Pt)` Divide both sides by `Pt` Solve for the Interest rate `(r),` using the formula`r` `=` `I/(Pt)` Formula for Interest Rate `=` $$\frac{450}{2{,}000\times5}$$ Plug in the known values `=` `0.045` `=` `4.5%` Convert to percentage `4.5%` interest rate -
Question 3 of 5
3. Question
How much interest is earned on `$500` at `6%` for six years?
- Interest Earned`=$ \ ` (180)
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Simple Interest Formula
`color(purple)(I)=color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)`Labelling the given values
Interest`=I=?`Principal Value`=P=$500`Rate`=r=6%` per annumTime Elapsed`=t=6` yearsFirst, express the rate as a decimal`6% = 0.06`Solve for the Interest `(I),` using the formula`color(purple)(I)` `=` `color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)` Simple Interest Formula `=` `color(forestgreen)($500) color(black)(times) color(royalblue)(0.06) color(black)(times) color(tomato)(6)` Plug in the known values `=` `$180` `$180` interest earned -
Question 4 of 5
4. Question
What is the interest rate if a principal of `$700` earns `$245` in interest in seven years?
- Interest rate`= \ ` (5)%
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Simple Interest Formula
`color(purple)(I)=color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)`Labelling the given values
Interest`=I=$245`Principal Value`=P=$700`Rate`=r=?` per annumTime Elapsed`=t=7` yearsSolve for the rate `(r),` using the formula`color(purple)(I)` `=` `color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)` Simple Interest Formula `color(purple)($245)` `=` `color(forestgreen)($700) color(black)(times) color(royalblue)(r) color(black)(times) color(tomato)(7)` Plug in the known values and simplify. `$245` `=` `$4,900timesr` Divide both sides by `$4,900`. `0.05` `=` `r` Reverse the two sides so the unknown variable `r` is on the left-hand side. `r` `=` `0.05times 100%` Multiply the rate by 100% to get the answer as a percent. `r` `=` `5%` The rate is `5%`. -
Question 5 of 5
5. Question
What will the final balance be for $700 invested at 3% for four years?
- Final Balance`=$ \ ` (784)
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Simple Interest Formula
`color(purple)(I)=color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)`Labelling the given values
Interest`=I=?`Principal Value`=P=$700`Rate`=r=3%` per annumTime Elapsed`=t=4` yearsFirst, express the rate as a decimal`3% = 0.03`Solve for the final balance by finding the Interest `(I)` earned and adding that to the Principal `(P)`.`color(purple)(I)` `=` `color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)` Simple Interest Formula `=` `color(forestgreen)($700) color(black)(times) color(royalblue)(0.03) color(black)(times) color(tomato)(4)` Plug in the known values `=` `$84` Final Balance `=` `$784` Now add the Interest `I=$84` to the Principal `P=$700` to get the final balance. `$784` final balance