Thorngate Industrial has committed to a capital equipment replacement fund by depositing $47,500 at the beginning of each quarter for 8 years. The fund earns 7.25% annually, compounded quarterly. Management needs to know the accumulated value at the end of the 8-year period to ensure sufficient capital for the planned machinery upgrade.
Correct Answers
future_value
$2,072,613.78
Step-by-Step Solution
Future Value of Annuity (annuity due): Payment (PMT): $47,500.00 Rate per period (r): 1.8125% Periods (n): 32 FVA (ordinary) = PMT × [(1+r)^n − 1] ÷ r FVA = $47,500.00 × [(1+1.8125%)^32 − 1] ÷ 1.8125% FVA = $47,500.00 × 42.857188 FVA (ordinary) = $2,035,716.42 Annuity due: FVA × (1+r) = $2,035,716.42 × 1.018125 = $2,072,613.78