Question 1209151: melinda invests her $80,000 winnings from publishers clearing house at a 2% annual percentage rate. find the amount of the investment at the end of 20 years and the amount of interest earned during the 20 years if the interest is compounded.
a. annually
b. quarterly
c. monthly
d. daily
Answer by textot(100)   (Show Source):
You can put this solution on YOUR website! **Formula for Compound Interest:**
* **A = P(1 + r/n)^(nt)**
Where:
* A = the future value of the investment/amount of money accumulated at the end of the period
* P = principal amount (initial investment) = $80,000
* r = annual interest rate (as a decimal) = 0.02
* n = number of times interest is compounded per year
* t = number of years = 20
**a) Annually Compounded**
* n = 1 (compounded once per year)
* A = 80000 * (1 + 0.02/1)^(1*20)
* A = 80000 * (1.02)^20
* A ≈ $148,594.74
* **Interest Earned:** $148,594.74 - $80,000 = $68,594.74
**b) Quarterly Compounded**
* n = 4 (compounded four times per year)
* A = 80000 * (1 + 0.02/4)^(4*20)
* A = 80000 * (1.005)^80
* A ≈ $149,452.79
* **Interest Earned:** $149,452.79 - $80,000 = $69,452.79
**c) Monthly Compounded**
* n = 12 (compounded twelve times per year)
* A = 80000 * (1 + 0.02/12)^(12*20)
* A = 80000 * (1.0016667)^240
* A ≈ $149,851.82
* **Interest Earned:** $149,851.82 - $80,000 = $69,851.82
**d) Daily Compounded**
* n = 365 (compounded 365 times per year)
* A = 80000 * (1 + 0.02/365)^(365*20)
* A = 80000 * (1.00005479)^7300
* A ≈ $149,927.93
* **Interest Earned:** $149,927.93 - $80,000 = $69,927.93
**Summary:**
| Compounding Frequency | Amount at End of 20 Years | Interest Earned |
|---|---|---|
| Annually | $148,594.74 | $68,594.74 |
| Quarterly | $149,452.79 | $69,452.79 |
| Monthly | $149,851.82 | $69,851.82 |
| Daily | $149,927.93 | $69,927.93 |
As you can see, the more frequently the interest is compounded, the slightly higher the final amount and the interest earned.
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