Respuesta :
The implied rate of interest is 4.00%
Explanation:
Principal (initial security worth)- $ 12,800
Final amount - $ 15,573.16
Time taken – 5 years
No additional deposition or withdrawal in between
∴ Rate of interest
This is the problem pertaining to compounding interest.
We know that for compound interest
Amount (A)= Principal(P)(1+R/100)ⁿ
Where R= rate of interest
N= time period
Thus, equation can be rearranged as
A/P=(1+R/100)ⁿ
Substituting the values of A, P and n as $15,573.16, $12800 and 5 years respectively
15573.16/12800=(1+R/100)⁵
Solving the above equation we would get R as 4%
The implied interest rate the investor will earn on the security is 4.33%
Explanation:
In the given problem,
- The worth of security currently is $12,800.
- Worth of security five years in the future is $15,573.16
- The profit/implied interest earned in five years = $15,573.16 - $12,800
- The profit/implied interest earned in five years = $2,773.16
The interest formulae is
- Interest = (Principal × Rate × Time)/100, so Rate% = (100 × Interest)/(Principal × Time)
By applying the above formulae in our case:
- Rate = ((100 * 2773.16) / (12800 * 5))
- Rate = (2,77,316) / (64,000)
- Rate = 4.33
Hence the implied interest rate the investor will earn on the security is 4.33%
