Calculating an Annuity-Due

 1) Solving the Total Amount You make monthly payments of \$100 in a 9% annuity-due. What is the total amount after 7 years? The payment per period is \$100 the total number of periods 'n' is: 12 periods per year for 7 years, equals 12*7 = 84 the interest rate we must use is .09 ÷ 12 = .0075 Putting these numbers into the formula: Total = 100 * [((1.0075)^85 -1)/.0075] -100 Total = 100 * [(1.88725097807133 -1)/.0075] -100 Total = 100 * (.88725097807133 / .0075) -100 Total = 11,830.0130409511 -100 Total = 11,730.01

 2) Solving the Periodic Payment (Using the data from question 1) A monthly 9% annuity-due is worth \$11,730.01 after 7 years? What was the periodic payment? ((1+r)(n+1) -1) ÷ r equals ((1+.0075)(85) -1) ÷ .0075 = (1.88725097807133 -1) ÷ .0075 = 0.88725097807133 ÷ .0075 = 118.30013040951 minus one equals 117.30013040951 Periodoc Payment = 11,730.01 ÷ 117.30013040951 Periodoc Payment = 100.00

 3) Solving for Years (Using the data from question 1) A 9% annuity-due with \$100 monthly investments is now worth \$11,730.01. How many years did this take? Log [rate * (total/periodic amount) + (1+rate)] Log [.0075 * (11,730.01/100) + 1.0075] = Log (1.88725075) = 0.275829606633691 Log (1+rate) Log (1.0075) = 0.00324505481314708 0.275829606633691 ÷ 0.00324505481314708 = 84.9999838265255 = 85 (rounded) 85 -1= 84 84/12 = 7 years

 4) Solving for Rate The annuity-due formula cannot be solved for rate. The annuity-due calculator solves for rate by using a trial and error process.

RETURN   TO   HOME   PAGE