Answer :
The interest amount (simple interest ) on the loan amount $5315 at 5% from 10th aug to 23rd dec. of same year is $105.50
How to calculate simple interest's amount?
If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
For this case, we're specified that:
- Principal amount = $5315
- Rate of interest = R% = 5% (assumingly annually, and simple interest).
- Time for which interest was applied: 10th aug to 23rd dec.( of same year assumingly)
Converting this time in terms of year, we get:
Aug has 31 days, Sept has 30 days, Oct. has 31 days, Nov has 30 days.
From 10th aug, till its last, there went 22 days.
Whole sept and oct and nov. was spent (30+31+30 = 91 days)
And then there were 22 days of december(23rd day not covered assumingly)
So, total days = 22+22+91 = 145 days.
Assuming averagely 365.25 days in an year, we get the average time for which the interest will be calculated as:
[tex]\dfrac{145}{365.25} \approx 0.397 \: \rm years[/tex]
Thus, we get: the amount of interest as:
[tex]I = \dfrac{P \times R \times T}{100}\\\\I \approx \dfrac{5315 \times 5\times 0.397}{100} \approx 105.50 \: \rm dollars[/tex]
Thus, the interest amount (simple interest ) on the loan amount $5315 at 5% from 10th aug to 23rd dec. of same year is $105.50
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