If I need to save for a boiler costing $14,000 in nine years at a 6% interest rate, how much should I set aside each year?

If I need to save for a boiler costing $14,000 in nine years at a 6% interest rate, how much should I set aside each year?

• A. $1,067.88
• B. $1,149.35
• C. $1,347.80
• D. $1,439.11

Answer: (B)

To determine how much you need to save each year to accumulate $14,000 in nine years at an interest rate of 6%, we can use the future value of an annuity formula. The future value of an annuity represents the total amount you will have after making regular deposits into an interest-bearing account for a specific period. The future value of an annuity formula is: \[ FV = P \left( \frac{(1 + r)^n - 1}{r} \right) \] where: - \( FV \) is the future value ($14,000), - \( P \) is the annual payment (the amount you need to set aside each year), - \( r \) is the interest rate per period (0.06), and - \( n \) is the number of periods (9 years). Rearranging the formula to solve for \( P \): \[ P = \frac{FV}{\left( \frac{(1 + r)^n - 1}{r} \right)} \] Substituting the values: \[ P = \frac{14000}{\left( \frac{(1 + 0.06)^9

To determine how much you need to save each year to accumulate $14,000 in nine years at an interest rate of 6%, we can use the future value of an annuity formula. The future value of an annuity represents the total amount you will have after making regular deposits into an interest-bearing account for a specific period.

The future value of an annuity formula is:

[

FV = P \left( \frac{(1 + r)^n - 1}{r} \right)

]

where:

• ( FV ) is the future value ($14,000),

• ( P ) is the annual payment (the amount you need to set aside each year),

• ( r ) is the interest rate per period (0.06), and

• ( n ) is the number of periods (9 years).

Rearranging the formula to solve for ( P ):

[

P = \frac{FV}{\left( \frac{(1 + r)^n - 1}{r} \right)}

]

Substituting the values:

[

P = \frac{14000}{\left( \frac{(1 + 0.06)^9