Mathematics: Asap a high-interest savings account pays 5.5% interest compounded annually. if $300 is deposited initially and again at the first of each year, which summation represents the money in the account 10 years after the initial deposit?

answer: 1%Step-by-step explanation:...

Asap a high-interest savings account pays 5.5% interest

brennarfa

04.01.2022

$\sum_{n=1}^{10} 316.5(1.055)^{n-1}$

Step-by-step explanation:

If $ 300 is deposited in an account which pays 5.5% interest compounded annually.

Then the amount after 1 year,

$A = 300(1+\frac{5.5}{100}) = 300(1+0.055) = 3000(1.055)=316.5$

Similarly, In the second year the amount in his account,

= 316.5 + 316.5(1.055)

In third year the amount in his account = 316.5 +316.5(1.055)+ 316(1.055)^2

In fourth year = 316.5 + 316.5(1.055) + 316(1.055)^2 + 316.5(1.055)^3

According to the question,

He repeat this process up to 10 years,

Hence, in the 10 years the amount in his account

= 316.5 + 316.5(1.055) + 316(1.055)^2 + 316.5(1.055)^3 --------- up to 10 terms,

= $\sum_{n=1}^{10} 316.5(1.055)^{n-1}$

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