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A sum of money is deposited in a bank at an interest rate of 4% p.a. compounded half-yearly. If the interest received after 1.5 years is$432. find the principal, correct to the nearest dollar.P + I = P(1 + i)^nP = principalI = interesti =interest rate per investment periodn = number of investment periodP = ?I = $432i = 0.04/2 = 0.02 (interest is compounded half-yearly)n = 3 (1.5 years, i.e. three 6-month period)P + 432 = P(1 + 0.02)^3P + 432 = P(1.02)^3P + 432 = 1.061208P432 = 1.061208P – P432 = 0.061208PP = 432/0.061208P = 7057.90The principal is $7058 (correct to the nearest dollar)Rough check:For 1 year ,7057.90 x 0.04 = $282.32For half a year 7057.90 x 0.02 = $141.16Total interest (based on simple interest) = $282.32 + $141.16= $423.48This is simple interest. We know that $432 is the compound interest and the compounded period is every 6 months, the  interest collected should be slightly more. We check so that the calculated result is acceptable. If for some reason the calculated   result is way off,either wrong formula is used or careless mistake comes into the calculation.
Comment:LauHenryk’s calculation is based on a term of 3 years and interest is compounded annually.Rough estimate:$3460 * 0.04 * 1.5 = $207.60 (simple interest) -- way off the $432. The answer is obviously wrong. That is why we have to go back and double check the input data and the formula used. No offence to LauHenryk.I do make mistake sometimes.

Let the principal be X.

432 = X(1 + 4%)^3 - X

432 = X[(1 + 4%)^3 -1]

X = 432 / [(1 + 4%)^3 - 1]

= 432 / 0.124864

= 3460 (cor. to the nearest dollar.)