certain amount of money has been deposited at the end of each quarter into an account that bears an interest of 7% p.a. after three years the total amount in the account is K6000. what was the amount deposited into the account at the end of each quarter? interest is compounded quarterly.

Answer 1

Let x be the amount deposited at the end of each quarter.

After 3 years, there will be a total of 12 quarters. So, the amount in the account after 3 years can be calculated using the formula for compound interest:

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

Where:
A = Total amount after 3 years (K6000)
P = Principal amount (amount deposited at the end of each quarter)
r = Annual interest rate (7% or 0.07)
n = Number of times interest is compounded per year (quarterly, so n = 4)
t = Number of years (3 years)

Plugging in the values:
6000 = x(1 + 0.07/4)^(4*3)

6000 = x(1.0175)^12

6000 = x(1.22504355)

x ≈ 6000 / 1.22504355

x ≈ K4896.31

Therefore, the amount deposited into the account at the end of each quarter was approximately K4896.31.