Stanley Bank offers a money market account that earns 1.85% compounded continuously: a) If $10,000 is invested in this type of account, how much will it be worth in 3 years? b) How long will it take for the account to be worth $15,000?
Answers
Answer:
a) $1056.33 b) 23 years
Step-by-step explanation:
a) 10000(1+1.85/100)^3=10565.33 (2d.p.)
b) let x be the no. of years
15000 = 10000(1+1.85/100)^x
1.5 = 1.0185^x
ln both sides
ln 1.5 = x ln 1.0185
x = ln 1.5/ln 1.0185
=22.11
=23 years (rounded up)
Final answer:
To calculate the future value of an investment using continuous compounding, you use the formula A = P*e^(rt). For a $10,000 investment at 1.85% annual interest, its value after 3 years is calculated by substituting the given values into the formula. To find out how many years it will take for the investment to reach $15,000, rearrange the formula to solve for t: t = ln(A/P)/r, and substitute the values.
Explanation:
The subject of your question is related to the mathematical concept known as continuouscompound interest, which Stanley Bank is applying to its money market account. In this concept, the formula is A = P×e^(rt), where A is the final amount that will be accumulated after t years, P is the principal amount or the initial investment, r is the interest rate in decimals (1.85% would be 0.0185), and e is Euler's number (~2.72).
a) To calculate the value of an investment of $10,000 after 3 years with an annual interest rate of 1.85%, you would use the formula: A = $10,000 × e^(0.0185 ×3). This will give you the total value of the investment after 3 years.
b) To calculate the number of years it will take for your investment to amount to $15,000 with the same interest rate, you would need to re-arrange the formula to solve for t: t = ln(A/P) / r. So, it would be calculated as: t = ln($15,000/$10,000) / 0.0185. This would give you the number of years it will take for your initial investment to reach $15,000.
Learn more about Continuous Compound Interest here:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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