Horizon Capital Corp. is establishing a sinking fund to retire a $5.2 million bond issue due in 10 years. The company will make quarterly deposits at the beginning of each quarter into an account earning 7.35% annually (compounded quarterly). Determine the quarterly payment required to accumulate exactly $5.2 million, then calculate the future value if the company deposits $98,500 per quarter under these same conditions.
Correct Answers
future_value
$5,849,996.94
Step-by-Step Solution
Future Value of Annuity (annuity due): Payment (PMT): $98,500.00 Rate per period (r): 1.8375% Periods (n): 40 FVA (ordinary) = PMT × [(1+r)^n − 1] ÷ r FVA = $98,500.00 × [(1+1.8375%)^40 − 1] ÷ 1.8375% FVA = $98,500.00 × 58.319216 FVA (ordinary) = $5,744,442.81 Annuity due: FVA × (1+r) = $5,744,442.81 × 1.018375 = $5,849,996.94