Question

If a security currently worth $12,800 will be worth $15,573.16 five years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made?

Answer 1

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%

Answer 2

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%