Question

A principal of $2,000 was invested in a savings account for 4 years. If the interest earned for the period was $240, what was the interest rate?

Answer 1

A= P(1+r%)ⁿ , where P = initial capital, r% = interest and n = number of years

After 4 years she earned $240 , so the new capital = $2240

2240 = 2000(1+r)⁴
2240/2000 = (1+r)⁴
1.12 = (1+r)⁴

ln(1.12) = ln(1+r)⁴
ln(1.12) = 4ln(1+r)

0.1133286 = 4ln(1+r)
0.02833 = ln(1+r)

(1+r%) = e⁰.⁰²⁸³³
r =  e⁰.⁰²⁸³³ - 1
r = 1.028737 - 1
r= 0.0287
or in % → r = 2.87%