You just won the lottery, which promises you $200,000 per year for the next 20 years. You receive the first payment today (hint:
1 answer:
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Answer:
The nominal interest rate is 16.5%
Explanation:
The nominal interest rate is the interest rate on an amount before consideration of inflation effects.
Mathematically, the nominal interest rate = n ×
where;
n = number of compounding periods per year
i = effective annual rate of interest
To calculate the nominal interest in this question, first of all, we have to calculate the total amount paid during the 36 monthly installment payments.
Total amount paid =517.78 × 36 = $18,640.08
Difference in amount = 18,640.08 - 16,000 = $2,640.08
Next let us calculate what percentage of the original amount ($16,000) is $2,640.08, to get the interest rate.
let the interest rate be X
X% of 16,000 = 2,640.08
X/100 × 16,000 = 2,640.08
X = 2,640.08 ÷ 160 = 16.5%
Note than 16.5% is the total interest rate for the 36 month period.
36 months = 3 years, therefore the overall interest over the course of the 3 years = 16.5%
Hence, effective annual interest rate (i) = 16.5 ÷ 3 = 5.5% = 0.055
Now, calculating nominal interest from the formula given above,
Nominal interest rate = n × ; n = 12 (monthly compounding)
= 12 ×
= (12 × 1.0045) - 1 = 11.05%
Therefore nominal interest = 11.05%