Lindsay is 25 years old and has a new job in web development. Lindsay wants to m

Question

Lindsay is 25 years old and has a new job in web development. Lindsay wants to make sure she is financially sound in 30 years, so she plans to invest the same amount into a retirement account at the end of every year for the next 30 years.

(a) Construct a data table in Excel that will show Lindsay the balance of her retirement account for various levels of annual investment and return. If Lindsay invests $11,500 at return of 5%, what would be the balance at the end of 20th year in the account? If required, round your answers to two decimal places. $ (b) Develop the two-way table in Excel for the balance at the end of 30th year in the account. Consider annual investment amounts of $5000 to $20,000 in increments of $1000, and returns of 0% to 12% in increments of 1%. Note that because Lindsay invests at the end of the year, there is no interest earned on the contribution for the year in which she contributes. Complete the below table. If required, round your answers to two decimal places. 7% 8% $5,000 $ $ $6,000 $ $ $7,000 $ $ $8,000 $ $ $9,000 $ $ $10,000 $ $ $11,000 $ $ $12,000 $ $ $13,000 $ $ $14,000 $ $ $15,000 $ $ $16,000 $ $ $17,000 $ $ $18,000 $ $ $19,000 $ $ $20,000 $ $

Explanation / Answer

SOLUTION

Back-up Theory

If a fixed sum, say P, is invested at the end of the year, at an annual return of r%, the amount at the end of t years = P(1 + i)t – 1, where i = r/100.

If this process is continued every year for t years, the total amount at the end of t years will be, A = P(1 + i)t – 1 + P(1 + i)t – 2 + P(1 + i)t – 3 + …… + P [Note: since investment is at the end of the year, the sum invested in the tth year does not earn any interest]

So, A = P{1 + (1 + i) + (1 + i)2 + (1 + i)3 + …… + (1 + i)t – 1}

              = P {(1 + i)t – 1}/{(1 + i) - 1} [applying the formula for sum of a GP]

         = (P/i) {(1 + i)t – 1} ……… (1)

For Part (a)

Substituting, P = 11500, I = 5/100 = 0.05, t = 20, in (1) above,

A = (11500/0.05)(1.0520 - 1) = 230000 x (2.6531 - 1) = 230000 x 1.6531

= 380213 ANSWER

For Part (b)

Just input the various values of P, i and t in (1) and generate the table.

NOTE

In all such calculations, compound interest is implicit. However, if the question specifically mentions ‘simple interest’,

A = Pt + i{(t - 1) + (t- 2) + ….. + 1 + 0} [Last investment does not earn interest.]

   = Pt + {it(t - 1)/2}

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