Meridian Capital Group establishes a sinking fund to retire a $5 million bond issue in 9 years. The firm commits to making quarterly deposits into a segregated account earning 7.25% annually (1.8125% per quarter). The first deposit occurs at the beginning of the first quarter, and deposits continue every quarter thereafter. Calculate the future value accumulated by the end of year 9 to determine if the sinking fund meets the $5 million obligation.
Correct Answers
future_value
$6,383,631.64
Step-by-Step Solution
Future Value of Annuity (annuity due): Payment (PMT): $125,000.00 Rate per period (r): 1.8125% Periods (n): 36 FVA (ordinary) = PMT × [(1+r)^n − 1] ÷ r FVA = $125,000.00 × [(1+1.8125%)^36 − 1] ÷ 1.8125% FVA = $125,000.00 × 50.159905 FVA (ordinary) = $6,269,988.11 Annuity due: FVA × (1+r) = $6,269,988.11 × 1.018125 = $6,383,631.64