Question

ian invested an amount of money at 3% per annum compound interest. At the end of 2 years the value of the investment was £2652.25 Work out the amount of money Ian invested.

Answer 1

the amount of money Ian invested is P = £2,500

Explanation:

The standard formula for compound interest is given as;

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

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case, Given that;

A = £2652.25

t = 2 years

n = 1 (semiannually)

r = 3% = 0.03

substituting the given values into equation 1;

`P = (A)/((1+r/n)^(nt)) ...........1\\P = (2652.25)/((1+0.03)^(2)) \\P = (2652.25)/((1.03)^(2)) \\`

P = £2,500

the amount of money Ian invested is P = £2,500