How long will it take $1750 to triple at 9.5% simple interest?

Question

John scored 5 points higher on his midterm, and 13 points higher on his final, than on his first exam. What did he score on his first exam if his average was 90?

Answer 1

Workings:

( * is multiply,
/ is divide.)

1) $1750 * 3 = $5250

2) $1750 * ( 9.5 / 100 ) = $166.25

3) $5250 / $166.25 = Approximately 31 and a half years.

I hope this helps.

Answer 2

1) That means the interest will be two times of 1750 = 2 x 1750 = 3500 dollars.

Since it is simple interest, the formula to be used is:

I = P.R.N where P is the principal, R the rate of interest per annum and N the number of years. Substituting the values,

3500 = 1750 x 9.5 x N

N = 9.5 x 3500 /1750 = 9.5 x 2 = 19 years

2) Average of three exams = 90

So total score = 3 x 90 = 270

John scored x , x + 5 and x + 13 marks in his first, mid-term and final exams. So, we can write,

x + x + 5 +x + 13 = 270

3x + 18 = 270

3x = 272 - 18 = 252

x = 252 / 3 = 84

John scored 84 marks in his first exam.

Answer 3

You seem to have at least two questions here.

For the interest rate and length of time calculations, the starting amount, $1750, isn't relevant to the amount of time it takes. Also, since you refer to the money tripling, this suggests that the interest is added to the balance and kept invested in the account.

Simple interest, Case 1: Assume "Simple interest" means that it does not get paid or added to the balance until the end of the period (e.g., a year, if 9.5% is an annual rate), and the amount earned on the last day of the year is the same as on the first day of the year. So, the account would grow 9.5% ($166.25) in the first year, and the account balance would then be $1,916.25, and interest in the second year would be 9.5% of that amount, or $182.04. This case is simple interest within the year, added to the balance at the end of the year, with simple interest in the subsequent year calculated on the adjusted balance. So, if "n" is an unknown number of years, the future value of the account will be the initial balance multiplied by:
(1.095)^n
that is, 1.095 to the n-th power. So, your question is: After how many years will 1.095^n = 3?
Answer 1 is: a bit over 12 years. (In a full 13 years, $1,750 earning 9.5% annually grows to $5,694, but in 12 years, it only grows to $5,200.)

Simple Interest, Case 2: Your assumption of "simple interest" might mean that it never compounds -- e.g., you invest $1,750 and earn 9.5% ($166.25) in the first year and then $166.25 in the second year, and so forth.
The question is: Why would anyone leave money in an account like this? The interest calculation would make mathematical sense if you take out the $166.25 each year, rather than leaving it in the account; thus, next year's interest will be the same amount, because the balance in the account hasn't changed. But, in that case, the money in the account never triples -- it always stays at $1,750.
So, in this scenario, I guess your question is: How many years of taking out the 9.5% interest allow the sum of the interest to be twice the amount of the investment (so, investment plus earnings equal 300% of the investment).
Answer 2: This would be 200% divided by 9.5%, or roughly 21 years.
Proof: On $1,750, annual interest is $166.25. Over 21 years, you receive 21 times 166.25, or $3,491.25, and if you also take out your account balance of $1,750, you've received a total of $5,241.25, which is just $8.75 short of $5,250 (triple your $1,750). If it is a simple interest account, and if an early withdrawal is permitted, you could earn the $8.75 in 5.26% of the 22nd year, or 19 days, assuming it is not a leap year. So, the second answer is 21 years and 19 days.

Was your question meant to be a simple one? Just asking out of interest.

Your second question, about exam scores, converts to the following equation, in which G represents John's first exam score:
(G) + (G + 5) + (G + 13) = 3 x 90 = 270
so, combining the left hand terms,
3G +18 = 270
since these are all divisible by 3, we can simplify it to
G + 6 = 90
so
G = 90 - 6 = 84, his first exam score.

If you want a more difficult division by 3, you can take
3G + 18 = 270
and subtract 18 from both sides, so
3G = 252
and then divide both sides by 3 to find that
G = 84, his first exam score.

I hope my explanations make it easier to do this sort of calculation on your own.

Answer 4

1)
$ 1750 x 3 = $5250 ==> triple of $ 1750
Simple Interest rate = 9.5% = 9.5/100 =.095
Yearly interest on $ 1750 at 9.5% =
1750 x .095 = $ 166.25

$ 5250/ 166.25 = 31.58 years or
31 years and 7 months

2)
Let x = score on his first exam
x + 5 = score on his midtem
x + 13 = score on his final
Average score =( x + (x+5) + (x + 13)) 3
If Average score = 90,
then
90 = (x + x + 5 + x + 13)/3
90 = (3x + 18)/3
Multiply both sides by 3
3(90 = (3x+18)/3
270 = 3x + 18
270-18 = 3x + 18 -18
252 = 3x
252/3 = 3x/3
84 = x
x = 84 ==> John score in the first exam

Answer 5

You write two problems:

Problem 1:
The formula to use is:
Vf = Vp x (1+ i)^n ……….(1)
Where Vf= future value; Vp= past value; I= interest by year; n=number of years (as exponent)

To replace data:
Vf=3Vp, Vp=$1750, I=9.5% è in (1)
3 = (0.095)^n ===> n = log3/log(0.095) = 12.1

===> we need 12 year and one month,
(for to have $1750 to triple with 9.5% by year and we started with $1750)


Problem 2
N= first score
We have next relation:
[N+ (N+5) +(N+13)] / 3 = 90
We can calculate:
[3N+18] / 3 = 90

===> N=84 (score in first exam)