Investment worksheet

1. Required annual return: 15.7%

1. Find the yearly return r that makes the end balance equal your target. There's no formula for this, so the calculator tries rates until one fits, turning each into a rate per month

   $\mathrm{\$13,000.00}\times {\left(1+0.01222998\right)}^{216}+\mathrm{\$420.00}\times \frac{{\left(1+0.01222998\right)}^{216}-1}{0.01222998}\times \left(1+0.01222998\right)$$=\mathrm{\$625,000.00}$

2. Turn the rate per month that fits back into a yearly return: (1 + i)^12 − 1

   $r$$=\mathrm{15.7045\%}$

3. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$625,000.00}-\mathrm{\$103,720.00}$$=\mathrm{\$521,280.00}$

2. Years needed: 23

1. Turn the 8% yearly return into a growth rate per month (i), since you add money every month

   $i$$=0.00643403$

2. Turn your regular contribution (C) into one helper amount, A = C ÷ i (times (1 + i) if you add money at the start). This makes the balance easy to write: after n periods, starting from P, it's (P + A)(1 + i)^n − A

   $A$$=\mathrm{\$81,597.38}$

3. Solve for n, the number of months. Logarithms (ln) undo the power, giving n = ln((target + A) ÷ (P + A)) ÷ ln(1 + i)

   $\frac{\text{ln(\$531,597.38 ÷ \$90,597.38)}}{\text{ln(1 + 0.00643403)}}$$=275.8998$

4. Round up to whole months: the first month that ends with the balance at or above the target

   $n$$=276$

5. Divide by 12 to turn months into years

   $\frac{276}{12}$$=23$

6. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$450,341.84}-\mathrm{\$153,900.00}$$=\mathrm{\$296,441.84}$

3. End balance: $382,841.38

1. Turn the 9% yearly return (r) into a monthly growth rate (i), since you add money every month: (1 + r)^(1/12) − 1

   $i$$=0.00720732$

2. See what your starting amount (P) grows to over 288 months: P × (1 + i)^n

   $\mathrm{\$9,000.00}\times {\left(1+0.00720732\right)}^{288}$$=\mathrm{\$71,199.75}$

3. Add up all 288 contributions, each with the growth it earns before the end

   $\mathrm{\$325.00}\times \frac{{\left(1+0.00720732\right)}^{288}-1}{0.00720732}$$=\mathrm{\$311,641.64}$

4. Add the two parts together to get your end balance

   $\mathrm{\$71,199.75}+\mathrm{\$311,641.64}$$=\mathrm{\$382,841.38}$

5. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$382,841.38}-\mathrm{\$102,600.00}$$=\mathrm{\$280,241.38}$

4. Years needed: 41

1. Turn the 9% yearly return into a growth rate per year (i), since you add money every year

   $i$$=0.09$

2. Turn your regular contribution (C) into one helper amount, A = C ÷ i (times (1 + i) if you add money at the start). This makes the balance easy to write: after n periods, starting from P, it's (P + A)(1 + i)^n − A

   $A$$=\mathrm{\$6,661.11}$

3. Solve for n, the number of years. Logarithms (ln) undo the power, giving n = ln((target + A) ÷ (P + A)) ÷ ln(1 + i)

   $\frac{\text{ln(\$606,661.11 ÷ \$18,261.11)}}{\text{ln(1 + 0.09)}}$$=40.6509$

4. Round up to whole years: the first year that ends with the balance at or above the target

   $n$$=41$

5. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$618,531.18}-\mathrm{\$34,150.00}$$=\mathrm{\$584,381.18}$

5. Required contribution per month: $693.20

1. Turn the 7% yearly return into a growth rate per month (i), since you add money every month

   $i$$=0.00565415$

2. See what your starting amount (P) grows to on its own over n periods: P × (1 + i)^n

   $\mathrm{\$10,000.00}\times {\left(1+0.00565415\right)}^{288}$$=\mathrm{\$50,723.67}$

3. Divide the amount still needed by what $1 added every month grows to over 288 months. That tells you how many dollars to add each time

   $\frac{\mathrm{\$550,000.00}-\mathrm{\$50,723.67}}{\frac{{\left(1+0.00565415\right)}^{288}-1}{0.00565415}}$$=\mathrm{\$693.20}$

4. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$550,000.00}-\mathrm{\$209,642.74}$$=\mathrm{\$340,357.26}$

6. End balance: $181,297.36

1. Turn the 9% yearly return (r) into a monthly growth rate (i), since you add money every month: (1 + r)^(1/12) − 1

   $i$$=0.00720732$

2. See what your starting amount (P) grows to over 168 months: P × (1 + i)^n

   $\mathrm{\$10,500.00}\times {\left(1+0.00720732\right)}^{168}$$=\mathrm{\$35,088.13}$

3. Add up all 168 contributions, each with the growth it earns before the end

   $\mathrm{\$450.00}\times \frac{{\left(1+0.00720732\right)}^{168}-1}{0.00720732}$$=\mathrm{\$146,209.23}$

4. Add the two parts together to get your end balance

   $\mathrm{\$35,088.13}+\mathrm{\$146,209.23}$$=\mathrm{\$181,297.36}$

5. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$181,297.36}-\mathrm{\$86,100.00}$$=\mathrm{\$95,197.36}$

7. Required contribution per year: $4,633.66

1. Turn the 6% yearly return into a growth rate per year (i), since you add money every year

   $i$$=0.06$

2. See what your starting amount (P) grows to on its own over n periods: P × (1 + i)^n

   $\mathrm{\$9,000.00}\times {\left(1+0.06\right)}^{30}$$=\mathrm{\$51,691.42}$

3. Divide the amount still needed by what $1 added every year grows to over 30 years. That tells you how many dollars to add each time

   $\frac{\mathrm{\$440,000.00}-\mathrm{\$51,691.42}}{\frac{{\left(1+0.06\right)}^{30}-1}{0.06}\times \left(1+0.06\right)}$$=\mathrm{\$4,633.66}$

4. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$440,000.00}-\mathrm{\$148,009.84}$$=\mathrm{\$291,990.16}$

8. Required annual return: 8.99%

1. Find the yearly return r that makes the end balance equal your target. There's no formula for this, so the calculator tries rates until one fits, turning each into a rate per month

   $\mathrm{\$7,500.00}\times {\left(1+0.00720307\right)}^{288}+\mathrm{\$460.00}\times \frac{{\left(1+0.00720307\right)}^{288}-1}{0.00720307}$$=\mathrm{\$500,000.00}$

2. Turn the rate per month that fits back into a yearly return: (1 + i)^12 − 1

   $r$$=\mathrm{8.9945\%}$

3. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$500,000.00}-\mathrm{\$139,980.00}$$=\mathrm{\$360,020.00}$

9. Required annual return: 6.56%

1. Find the yearly return r that makes the end balance equal your target. There's no formula for this, so the calculator tries rates until one fits, turning each into a rate per month

   $\mathrm{\$9,000.00}\times {\left(1+0.00531252\right)}^{336}+\mathrm{\$425.00}\times \frac{{\left(1+0.00531252\right)}^{336}-1}{0.00531252}\times \left(1+0.00531252\right)$$=\mathrm{\$450,000.00}$

2. Turn the rate per month that fits back into a yearly return: (1 + i)^12 − 1

   $r$$=\mathrm{6.5646\%}$

3. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$450,000.00}-\mathrm{\$151,800.00}$$=\mathrm{\$298,200.00}$

10. Required annual return: 8.51%

1. Find the yearly return r that makes the end balance equal your target. There's no formula for this, so the calculator tries rates until one fits, turning each into a rate per month

   $\mathrm{\$11,000.00}\times {\left(1+0.00682847\right)}^{264}+\mathrm{\$450.00}\times \frac{{\left(1+0.00682847\right)}^{264}-1}{0.00682847}\times \left(1+0.00682847\right)$$=\mathrm{\$400,000.00}$

2. Turn the rate per month that fits back into a yearly return: (1 + i)^12 − 1

   $r$$=\mathrm{8.509\%}$

3. Find how much came from growth: the end balance minus everything you put in

   $\mathrm{\$400,000.00}-\mathrm{\$129,800.00}$$=\mathrm{\$270,200.00}$