Rate (= [i]r[/i]) can be solved, if capital (= [i]k[/i]), interest rate (= [i]i[/i]) and interest time (= [i]t[/i]) are known. [br][br]  [math]\LARGE \textcolor{blue}{r=k\cdot i\cdot t.}[/math] [br][br][i][color=#0000ff]Increased capital (K)[/color][/i] is the capital plus the rate: [br][br]  [math]\LARGE \textcolor{blue}{K=k+r.}[/math][br][br]If the interest rate means annual interest, it is shortly with p.a. (= per annum). For example, it may be said in the contract, that rate for 3 months is 2.8% p.a. It means that interest rate for a year is 2.8% and for a three-month period, the interest is [math]\Large \frac{1}{4}\cdot 2.8\%=0.7\%.[/math][br]

Linda invested 6500€ to the account with interest rate of 3.5%. What is the annual rate?[br][br][i]k[/i] = 6500 €,[br][i]i[/i] = 3.5%/year = 0.035/year,[br][i]t[/i] = 1 year[br][br]  [math]\Large r = k\cdot i\cdot t=6500€\cdot \frac{0.0350}{\text{year}}\cdot 1\text{ year}= 227.50€.[/math]

Define the rate of a loan for Jan 20 - March 15 (not a leap-year) for each interest time, if the interest rate is 6.8% and the loan is 9800€. [br][br]We already solved the interest time for each case in Example 1. [br][i]i [/i]= 0.068 and [i]k[/i] = 9800 euros[br][br][table][tr][td][/td][td]Interest time [/td][td]Rate[/td][td][/td][td][/td][/tr][tr][td][b]real/360: [/b][/td][td]54/360[/td][td][math]\Large r= 9800€\cdot 0.068\cdot \frac{54}{360} = 99.96€[/math][/td][td][/td][td][/td][/tr][tr][td][b]real/365:[/b][/td][td]54/365[/td][td][math]\Large r= 9800€\cdot 0.068\cdot \frac{54}{365} = 98.59€[/math][/td][td][/td][td][/td][/tr][tr][td][b]30/360:[/b][/td][td]55/360[/td][td][math]\Large r= 9800€\cdot 0.068\cdot \frac{55}{360} = 101.81€[/math][/td][td][/td][td][/td][/tr][/table][br]The best for the customer is the case 2. [br]

A company had to pay residual tax for 4145.60€. The due date was December 4 but it was actually paid next year in January 20. Penalty interest is 8.0% and it is calculated by 30/360.[br][br]Interest time consists of days in December (30 - 4 = 26) and in January (20) with total of 46. Thus, the penalty rate is[br][br][math]\Large r=4145.60€\cdot 0.08\cdot \frac{46}{360}=42.38€[/math] [br][br]The total residual tax with penalty interest is[br][br][math]\Large K=k+r=4145.60€+42.38€=4187.98€[/math]

The reference rate (=viitekorko) for a housing loan is euribor 12 months, which happened to be 3.150%. The bank margin is 0.8%. What is the rate for the August, if the amount of loan is 107500€ at the end of July. [br][br]With euribor the interest time is calculated with real/360. There is 31 days in August, so the interest time is [math]\Large \frac{31}{360}.[/math] Interest rate is the euribor plus margin, so [math]\Large 3.150\%+0.8\%=3.950\%.[/math][br][br]Thus, the rate is[br][br][math]\Large r=107500€\cdot 0.0395\cdot\frac{31}{360}=365.65€[/math].[br][br]The calculators in Internet use, quite often, interest time 30/360. Then, the rate would be[br][br][br][math]\Large r=107500€\cdot 0.0395\cdot\frac{30}{360}=353.85€[/math].