University Maths Question

Let r denote the interest rate per annum. We obtain the monthly interest rate by r /12*.

Let D denote the amount of principal and I(2) denote the amount of interest to receive in 2 years.

The total amount of money in the account for any period is the sum of the principal and interest. Therefore there will be $ D + I(2) in the end of the 2-year investment horizon.

It follows that

D* (1 + r /12)^{2*12} = D + I(2),

D = I(2) / [(1 + r /12)^{2*12} - 1]

D = 5720/ [1.005^{24} - 1]

D = $44982.778

* We do not use the effective monthly interest rate for bank account accumulation. In fact the effective monthly interest rate would not give us the required D.