Question

How much should you invest each month in order to have $600,000 if your rate of return is 3.7% compounded monthly and you want to achieve your goal in 40 years?

How much interest will you earn?

How much should you invest each month in order to have $600,000 if you want to achieve your goal in 20 years?

If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?

Answer 1

Future Value = C*[(1+i)^n - 1]/(i)

Where

Future value = 600000

C - Cash flow per period (x)

i - interest rate per annum (3.7%)

n - number of payments (40*12 = 480)

600000 = x*[(1+0.037/12)^(40*12) - 1]/(0.037/12)

600000*0.037/12 = x*[(1+0.037/12)^(40*12) - 1]

1850 =x*[(1+0.003083)^(480) - 1]

1850 = x*[1.003083^480 - 1]

1850 = x*[4.382954 - 1]

1850 = x*3.382954

x = 1850/3.382954

= $ 546.86

Interest amount = Future value - installment amount * no. of payment

= 600000 - 546.86*480

= 600000 - 262498.2

= 337507

Part 2

Future value = 600000

C - Cash flow per period (x)

i - interest rate per annum (3.7%)

n - number of payments (20*12 = 240)

600000 = x*[(1+0.037/12)^(20*12) - 1]/(0.037/12)

600000*0.037/12 = x*[(1+0.037/12)^(20*12) - 1]

1850 =x*[(1+0.003083)^(240) - 1]

1850 = x*[1.003083^240 - 1]

1850 = x*[2.093384 - 1]

1850 = x*1.093384

x = 1850/1.093384

= $ 1692

Part 3

My savings worth after 10 years will be -

Future value after 10 years = 1692*[(1+0.037/12)^120 - 1]/(0.037/12)

= 1692*[1.003083^120 -1]/(0.003083)

= 1692*[1.446853 - 1]/(0.003083)

= 1692*0.446853/0.003083

= 1692*144.941

= $ 245240(approx)

Please check with your answer and let me know.