Part 2: Sinking Funds Assume that you wish to save $1,000,000 in a sinking fund

Question

Part 2: Sinking Funds Assume that you wish to save $1,000,000 in a sinking fund in 30 years. The account pays 7.5% compounded monthly. What should be your monthly payment? assume that you wish to save $1,000,000 in a sinking fund in 30 years. The account pays 8% compounded monthly. What should be your monthly payment? Notice that the interest rate changes by only 0.5%. How much less do you have to pay per month just by increasing the interest rate from 7.5% to 8%? Are you surprised at this figure? Why or why not?

Explanation / Answer

Given : accumulated amount = $1000000 , n = 30 years = 30×12 = 360 months , r = 7.5 %

Solution:

The monthly payment can be given as :

P = (1,000,000)/[{(1+0.075)360 -1}/0.075]

= $194.3

If interest rate increased by 0.5% then

r = 8% = 0.08

Then

P = (1,000,000)/[{(1+0.08)360 -1}/0.08]

P = $206.29

Hence monthly payment incresed by ($206.29-194.3)= $11.99

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