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Consider the following scenario: You would like to save up $50,000 after 10 years and plan to set up a structured savings plan to make monthly payments at 4.125% interest annually, compounded monthly
What lump sum amount would you need to invest at this interest rate in order to have $50,000 after 10 years?

Answer :

IthaloAbreu

Answer:

$ 388.77

Step-by-step explanation:

First, let's change the annually interest(ia) for monthy (im):

(1+ im)¹² = 1 + ia

(1 + im)¹² = 1 + 0.04125

1 + im = [tex]1.04125^{1/12}[/tex]

1 + im = 1.00337

im = 0.00337

im = 0.337%

The total amount (A) of the investment can be calculated by:

[tex]A = R*(\frac{(1+i)^n -1}{i})[/tex]

Where R is the amount invested by month, n is the number of months, and i is the interest.

10 years = 10*12 = 120 months

[tex]A = R*(\frac{(1+0.00337)^120 -1}{0.00337})[/tex]

50,000= R*147.59

R = $ 388.77

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