Question

Ella invests £7000 for 2 years in an account paying compound interest.

In the first year, the rate of interest is 3%
In the second year, the rate of interest is 1.5%

Work out the value of Ella's investment at the end of 2 years.

Answer 1

The formula for the future value of a single sum is:

F = P * (1 + r/n)^(nt)

Where:

F is the future value

P is the principal (the initial deposit)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For our calculation, we have:

P = £7000

r1 = 3% = 0.03

r2 = 1.5% = 0.015

n = 1 (annual compounding)

t1 = 1 (first year)

t2 = 1 (second year)

So, the future value of Ella's investment at the end of the first year is:

F1 = £7000 * (1 + 0.03/1)^(1 * 1) = £7000 * (1.03)^1 = £7,210

And the future value of Ella's investment at the end of the second year is:

F2 = £7,210 * (1 + 0.015/1)^(1 * 1) = £7,210 * (1.015)^1 = £7,333.15

So, at the end of 2 years, the value of Ella's investment is £7,333.15.

Explanation: