Ndiba invests a sum of money in a savings account with a fixed annual interest rate of 4.61% compounded 3 times per year. After 6 years, the balance reaches 5485.85. What was the amount of the initial investment?

Answer:the amount of the initial investment was $4165

Step-by-step explanation:

Let P represent the Initial amount of money invested. This means that the principal is P

It was compounded 3 times in a year. So

n = 3

The rate at which the principal was compounded is 4.61%. So

r = 4.61/100 = 0.0461

It was compounded for 6 years. So

t = 6

The formula for compound interest is

A = P (1+r/n) ^nt

A = total amount in the account at the end of t years. After 6 years, the balance reaches $5485.85. It means that

A = 5485.85

Therefore

5485.85 = P (1+0.0461/3) ^3 * 6

5485.85 = P (1.0154) ^18

P = 5485.85/1.317 = 4165.4