Annuity worksheet

1. Present value: $72,844.79

1. Find the interest rate for each month (i): divide the yearly rate by 12, because interest is added with each payment

   $i$$=\frac{0.08}{12}$$=0.00666667$

2. Count the payments (N): 12 a year for 17 years

   $N$$=12\times 17$$=204$

3. Shrink each payment back to what it's worth today, then add them all up. Then multiply by (1 + i), because each payment is made at the start of its period

   $\mathrm{\$650.00}\times \frac{1-{\left(1+0.00666667\right)}^{\mathrm{-204}}}{0.00666667}\times \left(1+0.00666667\right)$$=\mathrm{\$72,844.79}$

4. Take the present value away from the plain total of the payments. The gap, called the discount, is the cost of waiting for the money

   $\mathrm{\$132,600.00}-\mathrm{\$72,844.79}$$=\mathrm{\$59,755.21}$

2. Future value: $57,836.81

1. Find the interest rate for each quarter (i): divide the yearly rate by 4, because interest is added with each payment

   $i$$=\frac{0.05}{4}$$=0.0125$

2. Count the payments (N): 4 a year for 18 years

   $N$$=4\times 18$$=72$

3. Grow each payment with interest to the end of the term, then add them all up

   $\mathrm{\$500.00}\times \frac{{\left(1+0.0125\right)}^{72}-1}{0.0125}$$=\mathrm{\$57,836.81}$

4. Take away what you paid in to see how much interest you earned

   $\mathrm{\$57,836.81}-\mathrm{\$36,000.00}$$=\mathrm{\$21,836.81}$

3. Payout per month: $2,240.37

1. Find the interest rate for each month (i): divide the yearly rate by 12, because interest is added with each payment

   $i$$=\frac{0.05}{12}$$=0.00416667$

2. Count the payments (N): 12 a year for 18 years

   $N$$=12\times 18$$=216$

3. Find the payment that uses up the balance exactly by the last payment, counting the interest it earns along the way. Then divide by (1 + i), because each payment comes at the start of its period

   $\frac{\frac{\mathrm{\$320,000.00}\times 0.00416667}{1-{\left(1+0.00416667\right)}^{\mathrm{-216}}}}{\left(1+0.00416667\right)}$$=\mathrm{\$2,240.37}$

4. Add up everything you receive over the whole term

   $\mathrm{\$2,240.37}\times 216$$=\mathrm{\$483,920.66}$

5. Take away the starting balance to see the interest it earned while paying out

   $\mathrm{\$483,920.66}-\mathrm{\$320,000.00}$$=\mathrm{\$163,920.66}$

4. Future value: $477,745.67

1. Find the interest rate for each month (i): divide the yearly rate by 12, because interest is added with each payment

   $i$$=\frac{0.06}{12}$$=0.005$

2. Count the payments (N): 12 a year for 28 years

   $N$$=12\times 28$$=336$

3. Grow each payment with interest to the end of the term, then add them all up

   $\mathrm{\$550.00}\times \frac{{\left(1+0.005\right)}^{336}-1}{0.005}$$=\mathrm{\$477,745.67}$

4. Take away what you paid in to see how much interest you earned

   $\mathrm{\$477,745.67}-\mathrm{\$184,800.00}$$=\mathrm{\$292,945.67}$

5. Payout per year: $22,057.22

1. Find the interest rate for each year (i): divide the yearly rate by 1, because interest is added with each payment

   $i$$=\frac{0.08}{1}$$=0.08$

2. Count the payments (N): 1 a year for 22 years

   $N$$=1\times 22$$=22$

3. Find the payment that uses up the balance exactly by the last payment, counting the interest it earns along the way

   $\frac{\mathrm{\$225,000.00}\times 0.08}{1-{\left(1+0.08\right)}^{\mathrm{-22}}}$$=\mathrm{\$22,057.22}$

4. Add up everything you receive over the whole term

   $\mathrm{\$22,057.22}\times 22$$=\mathrm{\$485,258.74}$

5. Take away the starting balance to see the interest it earned while paying out

   $\mathrm{\$485,258.74}-\mathrm{\$225,000.00}$$=\mathrm{\$260,258.74}$

6. Future value: $45,701.96

1. Find the interest rate for each quarter (i): divide the yearly rate by 4, because interest is added with each payment

   $i$$=\frac{0.06}{4}$$=0.015$

2. Count the payments (N): 4 a year for 15 years

   $N$$=4\times 15$$=60$

3. Grow each payment with interest to the end of the term, then add them all up

   $\mathrm{\$475.00}\times \frac{{\left(1+0.015\right)}^{60}-1}{0.015}$$=\mathrm{\$45,701.96}$

4. Take away what you paid in to see how much interest you earned

   $\mathrm{\$45,701.96}-\mathrm{\$28,500.00}$$=\mathrm{\$17,201.96}$

7. Future value: $147,275.95

1. Find the interest rate for each month (i): divide the yearly rate by 12, because interest is added with each payment

   $i$$=\frac{0.05}{12}$$=0.00416667$

2. Count the payments (N): 12 a year for 18 years

   $N$$=12\times 18$$=216$

3. Grow each payment with interest to the end of the term, then add them all up. Then multiply by (1 + i), because each payment is made at the start of its period

   $\mathrm{\$420.00}\times \frac{{\left(1+0.00416667\right)}^{216}-1}{0.00416667}\times \left(1+0.00416667\right)$$=\mathrm{\$147,275.95}$

4. Take away what you paid in to see how much interest you earned

   $\mathrm{\$147,275.95}-\mathrm{\$90,720.00}$$=\mathrm{\$56,555.95}$

8. Payout per month: $2,112.29

1. Find the interest rate for each month (i): divide the yearly rate by 12, because interest is added with each payment

   $i$$=\frac{0.06}{12}$$=0.005$

2. Count the payments (N): 12 a year for 18 years

   $N$$=12\times 18$$=216$

3. Find the payment that uses up the balance exactly by the last payment, counting the interest it earns along the way. Then divide by (1 + i), because each payment comes at the start of its period

   $\frac{\frac{\mathrm{\$280,000.00}\times 0.005}{1-{\left(1+0.005\right)}^{\mathrm{-216}}}}{\left(1+0.005\right)}$$=\mathrm{\$2,112.29}$

4. Add up everything you receive over the whole term

   $\mathrm{\$2,112.29}\times 216$$=\mathrm{\$456,255.30}$

5. Take away the starting balance to see the interest it earned while paying out

   $\mathrm{\$456,255.30}-\mathrm{\$280,000.00}$$=\mathrm{\$176,255.30}$

9. Payout per year: $14,080.81

1. Find the interest rate for each year (i): divide the yearly rate by 1, because interest is added with each payment

   $i$$=\frac{0.06}{1}$$=0.06$

2. Count the payments (N): 1 a year for 25 years

   $N$$=1\times 25$$=25$

3. Find the payment that uses up the balance exactly by the last payment, counting the interest it earns along the way

   $\frac{\mathrm{\$180,000.00}\times 0.06}{1-{\left(1+0.06\right)}^{\mathrm{-25}}}$$=\mathrm{\$14,080.81}$

4. Add up everything you receive over the whole term

   $\mathrm{\$14,080.81}\times 25$$=\mathrm{\$352,020.23}$

5. Take away the starting balance to see the interest it earned while paying out

   $\mathrm{\$352,020.23}-\mathrm{\$180,000.00}$$=\mathrm{\$172,020.23}$

10. Present value: $86,522.98

1. Find the interest rate for each month (i): divide the yearly rate by 12, because interest is added with each payment

   $i$$=\frac{0.04}{12}$$=0.00333333$

2. Count the payments (N): 12 a year for 15 years

   $N$$=12\times 15$$=180$

3. Shrink each payment back to what it's worth today, then add them all up

   $\mathrm{\$640.00}\times \frac{1-{\left(1+0.00333333\right)}^{\mathrm{-180}}}{0.00333333}$$=\mathrm{\$86,522.98}$

4. Take the present value away from the plain total of the payments. The gap, called the discount, is the cost of waiting for the money

   $\mathrm{\$115,200.00}-\mathrm{\$86,522.98}$$=\mathrm{\$28,677.02}$