Question 1186455: On her recent birthday, April 22, 2001, Nicole was given by her mother a certain sum of money as birthday present. She decided to invest the said amount on 20% exact simple interest. If the account will mature on Christmas day at an amount of P 10,000.00, How much did Nicole receive from her mother on her birthday
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the amount Nicole received from her mother:
1. **Determine the time period:**
* Nicole's birthday: April 22, 2001
* Maturity date: December 25, 2020
The time period is from April 22, 2001, to December 25, 2020. This is a span of 19 years, 8 months, and 3 days. In terms of exact simple interest, we count the exact number of days.
From April 22, 2001 to December 25, 2020, there are 7164 days.
2. **Use the simple interest formula:**
* Future Value (FV) = Principal (P) + Interest (I)
* Interest (I) = P * r * t
* Where:
* FV = Future Value (P 10,000.00)
* P = Principal (what we want to find)
* r = interest rate (20% or 0.20)
* t = time in years (7164 days / 365 days/year ≈ 19.627 years)
3. **Substitute and solve for P:**
* FV = P + P * r * t
* FV = P(1 + rt)
* P = FV / (1 + rt)
* P = 10,000 / (1 + (0.20 * 19.627))
* P = 10,000 / (1 + 3.9254)
* P = 10,000 / 4.9254
* P ≈ 2029.92
Therefore, Nicole received approximately **P 2,029.92** from her mother on her birthday.
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
On her recent birthday, April 22, 2001, Nicole was given by her mother a certain sum of money as birthday present.
She decided to invest the said amount on 20% exact simple interest. If the account will mature
on Christmas day at an amount of P 10,000.00, How much did Nicole receive from her mother on her birthday
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To me, it is unclear why the tutor @CPhill uses the year 2020 as the maturity year.
Nothing in the problem points in it.
The problem says "On her recent birthday, April 22, 2001 . . . ",
so, the expected year, when the account is mature, is the year 2001.
It is very unnatural that a deposit has 20% simple interest during about 20 years.
So, the solution and the answer in the post by @CPhill are irrelevant, in my view,
reflecting his fantasy, not the problem's context.
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