Pathside Industrial is establishing a sinking fund to replace aging equipment in 8 years. The company commits to depositing $47,500 at the beginning of each quarter into an account earning 6.75% annually (compounded quarterly). Calculate the future value of these annuity due payments to determine whether the accumulated fund will meet the projected $1.85 million replacement cost.
Correct Answers
future_value
$2,027,356.28
Step-by-Step Solution
Future Value of Annuity (annuity due): Payment (PMT): $47,500.00 Rate per period (r): 1.6875% Periods (n): 32 FVA (ordinary) = PMT × [(1+r)^n − 1] ÷ r FVA = $47,500.00 × [(1+1.6875%)^32 − 1] ÷ 1.6875% FVA = $47,500.00 × 41.972892 FVA (ordinary) = $1,993,712.39 Annuity due: FVA × (1+r) = $1,993,712.39 × 1.016875 = $2,027,356.28