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?

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%