College Savings worksheet

1. Monthly saving needed: $433.12

1. Count the years until college starts, since that is how long your savings have to grow

   $20-4$$=16$

2. Grow today's cost by 4% a year to the first year of college

   $\mathrm{\$19,000.00}\times {\left(1+0.04\right)}^{16}$$=\mathrm{\$35,586.64}$

3. Add up all 5 years' bills. Each year costs a little more, after another year of price rises

   $\text{5 yearly bills}$$=\mathrm{\$192,748.74}$

4. Money left invested keeps earning 6% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.06)^k}$$=\mathrm{\$171,344.25}$

5. Cover 90% of it from savings

   $\mathrm{90\%}\times \mathrm{\$171,344.25}$$=\mathrm{\$154,209.83}$

6. Grow what is already saved for 192 months at the monthly equivalent of 6% (i = 0.00486755)

   $\mathrm{\$6,750.00}\times {\left(1+0.00486755\right)}^{192}$$=\mathrm{\$17,147.37}$

7. Divide the gap still to fill by what $1 a month grows to over 192 months. This gives the monthly saving

   $\frac{\mathrm{\$154,209.83}-\mathrm{\$17,147.37}}{\frac{{\left(1+0.00486755\right)}^{192}-1}{0.00486755}}$$=\mathrm{\$433.12}$

2. Monthly saving needed: $736.78

1. Count the years until college starts, since that is how long your savings have to grow

   $15-4$$=11$

2. Grow today's cost by 7% a year to the first year of college

   $\mathrm{\$25,000.00}\times {\left(1+0.07\right)}^{11}$$=\mathrm{\$52,621.30}$

3. Add up all 4 years' bills. Each year costs a little more, after another year of price rises

   $\mathrm{\$52,621.30}+\mathrm{\$56,304.79}+\mathrm{\$60,246.13}+\mathrm{\$64,463.35}$$=\mathrm{\$233,635.57}$

4. Money left invested keeps earning 7% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.07)^k}$$=\mathrm{\$210,485.20}$

5. Cover 80% of it from savings

   $\mathrm{80\%}\times \mathrm{\$210,485.20}$$=\mathrm{\$168,388.16}$

6. Grow what is already saved for 132 months at the monthly equivalent of 7% (i = 0.00565415)

   $\mathrm{\$11,600.00}\times {\left(1+0.00565415\right)}^{132}$$=\mathrm{\$24,416.28}$

7. Divide the gap still to fill by what $1 a month grows to over 132 months. This gives the monthly saving

   $\frac{\mathrm{\$168,388.16}-\mathrm{\$24,416.28}}{\frac{{\left(1+0.00565415\right)}^{132}-1}{0.00565415}}$$=\mathrm{\$736.78}$

3. Monthly saving needed: $361.11

1. Count the years until college starts, since that is how long your savings have to grow

   $21-5$$=16$

2. Grow today's cost by 3% a year to the first year of college

   $\mathrm{\$25,000.00}\times {\left(1+0.03\right)}^{16}$$=\mathrm{\$40,117.66}$

3. Add up all 4 years' bills. Each year costs a little more, after another year of price rises

   $\mathrm{\$40,117.66}+\mathrm{\$41,321.19}+\mathrm{\$42,560.83}+\mathrm{\$43,837.65}$$=\mathrm{\$167,837.33}$

4. Money left invested keeps earning 6% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.06)^k}$$=\mathrm{\$153,785.84}$

5. Cover 90% of it from savings

   $\mathrm{90\%}\times \mathrm{\$153,785.84}$$=\mathrm{\$138,407.25}$

6. Grow what is already saved for 192 months at the monthly equivalent of 6% (i = 0.00486755)

   $\mathrm{\$9,500.00}\times {\left(1+0.00486755\right)}^{192}$$=\mathrm{\$24,133.34}$

7. Divide the gap still to fill by what $1 a month grows to over 192 months. This gives the monthly saving

   $\frac{\mathrm{\$138,407.25}-\mathrm{\$24,133.34}}{\frac{{\left(1+0.00486755\right)}^{192}-1}{0.00486755}}$$=\mathrm{\$361.11}$

4. Monthly saving needed: $518.75

1. Count the years until college starts, since that is how long your savings have to grow

   $20-5$$=15$

2. Grow today's cost by 5% a year to the first year of college

   $\mathrm{\$30,000.00}\times {\left(1+0.05\right)}^{15}$$=\mathrm{\$62,367.85}$

3. Add up all 3 years' bills. Each year costs a little more, after another year of price rises

   $\mathrm{\$62,367.85}+\mathrm{\$65,486.24}+\mathrm{\$68,760.55}$$=\mathrm{\$196,614.63}$

4. Money left invested keeps earning 6% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.06)^k}$$=\mathrm{\$185,343.96}$

5. Cover 90% of it from savings

   $\mathrm{90\%}\times \mathrm{\$185,343.96}$$=\mathrm{\$166,809.56}$

6. Grow what is already saved for 180 months at the monthly equivalent of 6% (i = 0.00486755)

   $\mathrm{\$7,500.00}\times {\left(1+0.00486755\right)}^{180}$$=\mathrm{\$17,974.19}$

7. Divide the gap still to fill by what $1 a month grows to over 180 months. This gives the monthly saving

   $\frac{\mathrm{\$166,809.56}-\mathrm{\$17,974.19}}{\frac{{\left(1+0.00486755\right)}^{180}-1}{0.00486755}}$$=\mathrm{\$518.75}$

5. Monthly saving needed: $306.97

1. Count the years until college starts, since that is how long your savings have to grow

   $20-5$$=15$

2. Grow today's cost by 4% a year to the first year of college

   $\mathrm{\$20,000.00}\times {\left(1+0.04\right)}^{15}$$=\mathrm{\$36,018.87}$

3. Add up all 4 years' bills. Each year costs a little more, after another year of price rises

   $\mathrm{\$36,018.87}+\mathrm{\$37,459.62}+\mathrm{\$38,958.01}+\mathrm{\$40,516.33}$$=\mathrm{\$152,952.84}$

4. Money left invested keeps earning 6% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.06)^k}$$=\mathrm{\$140,048.92}$

5. Cover 80% of it from savings

   $\mathrm{80\%}\times \mathrm{\$140,048.92}$$=\mathrm{\$112,039.14}$

6. Grow what is already saved for 180 months at the monthly equivalent of 6% (i = 0.00486755)

   $\mathrm{\$10,000.00}\times {\left(1+0.00486755\right)}^{180}$$=\mathrm{\$23,965.58}$

7. Divide the gap still to fill by what $1 a month grows to over 180 months. This gives the monthly saving

   $\frac{\mathrm{\$112,039.14}-\mathrm{\$23,965.58}}{\frac{{\left(1+0.00486755\right)}^{180}-1}{0.00486755}}$$=\mathrm{\$306.97}$

6. Monthly saving needed: $408.12

1. Count the years until college starts, since that is how long your savings have to grow

   $20-4$$=16$

2. Grow today's cost by 6% a year to the first year of college

   $\mathrm{\$26,000.00}\times {\left(1+0.06\right)}^{16}$$=\mathrm{\$66,049.14}$

3. Add up all 3 years' bills. Each year costs a little more, after another year of price rises

   $\mathrm{\$66,049.14}+\mathrm{\$70,012.09}+\mathrm{\$74,212.82}$$=\mathrm{\$210,274.05}$

4. Money left invested keeps earning 6% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.06)^k}$$=\mathrm{\$198,147.43}$

5. Cover 78% of it from savings

   $\mathrm{78\%}\times \mathrm{\$198,147.43}$$=\mathrm{\$154,555.00}$

6. Grow what is already saved for 192 months at the monthly equivalent of 6% (i = 0.00486755)

   $\mathrm{\$10,000.00}\times {\left(1+0.00486755\right)}^{192}$$=\mathrm{\$25,403.52}$

7. Divide the gap still to fill by what $1 a month grows to over 192 months. This gives the monthly saving

   $\frac{\mathrm{\$154,555.00}-\mathrm{\$25,403.52}}{\frac{{\left(1+0.00486755\right)}^{192}-1}{0.00486755}}$$=\mathrm{\$408.12}$

7. Monthly saving needed: $1,644.05

1. Count the years until college starts, since that is how long your savings have to grow

   $12-5$$=7$

2. Grow today's cost by 5% a year to the first year of college

   $\mathrm{\$27,500.00}\times {\left(1+0.05\right)}^7$$=\mathrm{\$38,695.26}$

3. Add up all 5 years' bills. Each year costs a little more, after another year of price rises

   $\text{5 yearly bills}$$=\mathrm{\$213,815.75}$

4. Money left invested keeps earning 5% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.05)^k}$$=\mathrm{\$193,476.31}$

5. Cover 90% of it from savings

   $\mathrm{90\%}\times \mathrm{\$193,476.31}$$=\mathrm{\$174,128.68}$

6. Grow what is already saved for 84 months at the monthly equivalent of 5% (i = 0.00407412)

   $\mathrm{\$7,000.00}\times {\left(1+0.00407412\right)}^{84}$$=\mathrm{\$9,849.70}$

7. Divide the gap still to fill by what $1 a month grows to over 84 months. This gives the monthly saving

   $\frac{\mathrm{\$174,128.68}-\mathrm{\$9,849.70}}{\frac{{\left(1+0.00407412\right)}^{84}-1}{0.00407412}}$$=\mathrm{\$1,644.05}$

8. Monthly saving needed: $717.08

1. Count the years until college starts, since that is how long your savings have to grow

   $18-6$$=12$

2. Grow today's cost by 5% a year to the first year of college

   $\mathrm{\$25,000.00}\times {\left(1+0.05\right)}^{12}$$=\mathrm{\$44,896.41}$

3. Add up all 5 years' bills. Each year costs a little more, after another year of price rises

   $\text{5 yearly bills}$$=\mathrm{\$248,081.00}$

4. Money left invested keeps earning 5% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.05)^k}$$=\mathrm{\$224,482.04}$

5. Cover 70% of it from savings

   $\mathrm{70\%}\times \mathrm{\$224,482.04}$$=\mathrm{\$157,137.43}$

6. Grow what is already saved for 144 months at the monthly equivalent of 5% (i = 0.00407412)

   $\mathrm{\$9,500.00}\times {\left(1+0.00407412\right)}^{144}$$=\mathrm{\$17,060.64}$

7. Divide the gap still to fill by what $1 a month grows to over 144 months. This gives the monthly saving

   $\frac{\mathrm{\$157,137.43}-\mathrm{\$17,060.64}}{\frac{{\left(1+0.00407412\right)}^{144}-1}{0.00407412}}$$=\mathrm{\$717.08}$

9. Monthly saving needed: $1,010.22

1. Count the years until college starts, since that is how long your savings have to grow

   $18-6$$=12$

2. Grow today's cost by 6% a year to the first year of college

   $\mathrm{\$27,000.00}\times {\left(1+0.06\right)}^{12}$$=\mathrm{\$54,329.30}$

3. Add up all 5 years' bills. Each year costs a little more, after another year of price rises

   $\text{5 yearly bills}$$=\mathrm{\$306,259.34}$

4. Money left invested keeps earning 6% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.06)^k}$$=\mathrm{\$271,646.52}$

5. Cover 84% of it from savings

   $\mathrm{84\%}\times \mathrm{\$271,646.52}$$=\mathrm{\$228,183.08}$

6. Grow what is already saved for 144 months at the monthly equivalent of 6% (i = 0.00486755)

   $\mathrm{\$9,000.00}\times {\left(1+0.00486755\right)}^{144}$$=\mathrm{\$18,109.77}$

7. Divide the gap still to fill by what $1 a month grows to over 144 months. This gives the monthly saving

   $\frac{\mathrm{\$228,183.08}-\mathrm{\$18,109.77}}{\frac{{\left(1+0.00486755\right)}^{144}-1}{0.00486755}}$$=\mathrm{\$1,010.22}$

10. Monthly saving needed: $1,134.00

1. Count the years until college starts, since that is how long your savings have to grow

   $18-5$$=13$

2. Grow today's cost by 5% a year to the first year of college

   $\mathrm{\$32,500.00}\times {\left(1+0.05\right)}^{13}$$=\mathrm{\$61,283.60}$

3. Add up all 4 years' bills. Each year costs a little more, after another year of price rises

   $\mathrm{\$61,283.60}+\mathrm{\$64,347.78}+\mathrm{\$67,565.17}+\mathrm{\$70,943.42}$$=\mathrm{\$264,139.96}$

4. Money left invested keeps earning 4% during college, so discount each later bill back to the start of college

   $\text{Σ bill ÷ (1 + 0.04)^k}$$=\mathrm{\$248,692.70}$

5. Grow what is already saved for 156 months at the monthly equivalent of 4% (i = 0.00327374)

   $\mathrm{\$11,000.00}\times {\left(1+0.00327374\right)}^{156}$$=\mathrm{\$18,315.81}$

6. Divide the gap still to fill by what $1 a month grows to over 156 months. This gives the monthly saving

   $\frac{\mathrm{\$248,692.70}-\mathrm{\$18,315.81}}{\frac{{\left(1+0.00327374\right)}^{156}-1}{0.00327374}}$$=\mathrm{\$1,134.00}$