What equal annual series of payments must be paid into a sin

What equal annual series of payments must be paid into a sinking fund in order t accumulate each given amount? $15,000 in 13 years at 5% compounded annually. $20,000 in eight years at 6% compounded annually. $5,000 in 25 years at 8% compounded annually. $4,000 in eight years at 6.85% compounded annually.

Solution

Sinking Fund:

Aside money over time, to invest annually for business sets. i.e. the principal plus the interest earned in the fund will be enough to replace the asset.

The formula for Compound Interest: F=P(1+r/n)^nt

(a) $15,000 in 13 years at 5%compoubded annually

F= $15,000 (1+5/100)^1*13

⁼$15,000 (21/20)¹³

⁼ $15,000 (1.05)¹³

⁼$15,000 (1.8856)

=$28284

(b) $20,000 in 8 years at 6% compounded annually

F = $20,000 (1+6/100)^1*8

⁼ $20,000 (1+0.06)⁸

⁼ $20,000 (1.06)⁸

⁼ $20,000(1.5938)

=$31876

(c) $5,000 in 25 years at 8% compounded annually

=$5,000 (1+8/100)^1*25

=$5,000 (1+0.08)²⁵

=$5,000(6.8484)

=$34242

(d) $4,000 in 8 years at 6.85% compounded annually

F= $4,000 (1+6.85/100)^1*8

= $4,000 (1+0.0685)⁸

= $4,000 (1.0685)⁸

= $4,000 (1.6990)

= $6796

The formula for Compound Interest: F=P(1+r/n)nt P =initial principal r = annual nominal interest rate n = number of times the interest is compounded per year t = number of years F = future amount after time t (a) $15,000 in 13 years at 5%compoubded annually F= $15,000 (1+5/100)1*13 =$15,000 (21/20)13 = $15,000 (1.05)13 =$15,000 (1.8856) =$28284