Question

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 1

$ 388.77

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 =
`1.04125^(1/12)`

1 + im = 1.00337

im = 0.00337

im = 0.337%

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

`A = R*(((1+i)^n -1)/(i))`

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

`A = R*(((1+0.00337)^120 -1)/(0.00337))`

50,000= R*147.59

R = $ 388.77