Your goal is to accumulate $100,000 in four years' time. What half-yearly deposit must you make into a savings account to reach your goal? Interest rates are 5% per half-year. Group of answer choices $2,264.88 $11,446.73 $23,201.18 $10,472.18
Question
Your goal is to accumulate $100,000 in four years' time. What half-yearly deposit must you make into a savings account to reach your goal? Interest rates are 5% per half-year.
Group of answer choices
$2,264.88
$11,446.73
$23,201.18
$10,472.18
Solution
To calculate the half-yearly deposit you must make into a savings account to reach your goal, we can use the formula for the present value of a series of regular payments:
PV = P * [1 - (1 + r)^-n] / r
where:
- PV is the present value ($100,000)
- P is the regular payment per period (what we're trying to find)
- r is the interest rate per period (5% or 0.05)
- n is the number of periods (4 years multiplied by 2 half-years per year)
Rearranging the formula to solve for P, we get:
P = PV * r / [1 - (1 + r)^-n]
Substituting the given values into the formula, we get:
P = $100,000 * 0.05 / [1 - (1 + 0.05)^-(4*2)]
Calculating this expression, we find that you must make a half-yearly deposit of approximately 11,446.73.
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