Pregunta
Greg buys a home for \( \$ 328,500 \). His home is predicted to increase in value \( 4 \% \) each year. What is the predicted value of his home in 30 years? \( \$ 994,878 \) \( \$ 1,003,716 \) \( \$ 1,065,456 \) \( \$ 1,158,324 \) Question 21 (4 points) Andrew pays \( \$ 1824 \) per year in tuition. How much should he budget monthly for it? \( \$ 35 \) \( \$ 76 \) \( \$ 124 \)
Ask by Schwartz Harrington. in the United States
Jan 27,2025
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Greg's home will be worth approximately \$1,065,456 in 30 years. Andrew should budget \$152 monthly for tuition.
Solución
To find the predicted value of Greg's home in 30 years, we need to calculate the future value of the home using the formula for compound interest:
\[ FV = PV \times (1 + r)^n \]
where:
- \( FV \) is the future value of the home,
- \( PV \) is the present value of the home (initial cost),
- \( r \) is the annual interest rate (4% in this case),
- \( n \) is the number of years (30 years in this case).
Given that the present value of the home is $328,500 and the annual interest rate is 4%, we can calculate the future value of the home in 30 years.
To find out how much Andrew should budget monthly for tuition, we need to divide the annual tuition by 12 to get the monthly amount.
Let's calculate the predicted value of Greg's home in 30 years and the monthly budget for Andrew's tuition.
Calculate the value by following steps:
- step0: Calculate:
\(328500\left(1+0.04\right)^{30}\)
- step1: Add the numbers:
\(328500\times 1.04^{30}\)
- step2: Convert the expressions:
\(328500\left(\frac{26}{25}\right)^{30}\)
- step3: Simplify:
\(328500\times \frac{26^{30}}{25^{30}}\)
- step4: Rewrite the expression:
\(125\times 2628\times \frac{26^{30}}{25^{30}}\)
- step5: Rewrite the expression:
\(5^{3}\times 2628\times \frac{26^{30}}{5^{60}}\)
- step6: Reduce the numbers:
\(2628\times \frac{26^{30}}{5^{57}}\)
- step7: Multiply:
\(\frac{2628\times 26^{30}}{5^{57}}\)
The predicted value of Greg's home in 30 years is approximately $1,065,456.
Now, let's calculate the monthly budget for Andrew's tuition by dividing the annual tuition by 12.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{1824}{12}\)
- step1: Reduce the numbers:
\(\frac{152}{1}\)
- step2: Calculate:
\(152\)
Andrew should budget $152 monthly for tuition.
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Simplifique esta solución Extra Insights
To find the predicted value of Greg's home after 30 years with a 4% annual increase, you can use the formula for compound interest: \[ V = P(1 + r)^t \] where \( V \) is the future value, \( P \) is the present value (\$328,500), \( r \) is the annual increase rate (0.04), and \( t \) is the number of years (30). Plugging in the numbers gives: \[ V = 328,500(1 + 0.04)^{30} \approx 1,065,456 \] For Andrew's tuition, to find out how much he should budget monthly, simply divide the yearly amount by 12. Thus, \[ \frac{1824}{12} = 152 \] For the options given, the closest and most accurate monthly budget would be \$152, allowing him to comfortably manage his tuition payments!
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