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Jose now has $500. How much would he have after 6 years if he leaves it invested at 7.0% with annual compounding?

a. $570,28
b. $892.93
c. $727.85
d. $750.50
e. $697.84 15.

User DragonBobZ
by
8.1k points

1 Answer

6 votes

Final answer:

Using the formula for compound interest, Jose would have approximately $750.60 after 6 years of investing $500 at a 7% annual interest rate with annual compounding. The closest answer choice provided is option d. $750.50.

Step-by-step explanation:

The question involves calculating the future value of an investment with compound interest. To find out how much Jose would have after 6 years when he leaves $500 invested at a 7.0% annual interest with annual compounding, we use the compound interest formula:

A = P(1 + r/n)nt

Where:

  • A = the future value of the investment/loan, including interest
  • P = the principal investment amount (the initial deposit or loan amount)
  • r = the annual interest rate (decimal)
  • n = the number of times that interest is compounded per year
  • t = the number of years the money is invested or borrowed for

In Jose's case:

  • P = $500
  • r = 7.0% or 0.07
  • n = 1 (since it is compounded annually)
  • t = 6

So the calculation is:

$500(1 + 0.07/1)1*6 = $500(1 + 0.07)6

Now calculating the compound amount:

A = $500(1.07)6

A = $500 * 1.501209

A ≈ $750.60

Therefore, the correct choice is option d, $750.50 - though there is a slight discrepancy due to rounding during the calculation.

User Spike Gronim
by
8.4k points
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