Question

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? Sigma-Summation Underscript n = 1 Overscript 10 EndScripts 300 (0. 055) Superscript n minus 1 Sigma-Summation Underscript n = 1 Overscript 10 EndScripts 305. 5 (1. 055) Superscript n minus 1 Sigma-Summation Underscript n = 1 Overscript 10 EndScripts 316. 5 (0. 055) Superscript n minus 1 Sigma-Summation Underscript n = 1 Overscript 10 EndScripts 316. 5 (1. 055) Superscript n minus 1.

Answer 1

For the given question, the summation that represents the money in account is:

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

The principal amount if compounded annually, the formula that represents the amount to be received after n years is:

$\rm A = P(1 + \dfrac{r}{100})^t$ where A is the amount received after compounding, P is the principal, r is the rate of interest and t is the tenure.

Solution:

Given:

Annual interest rate(r) is 5.5%

Principal is(P) $300

Tenure is(t) 10 years

On substituting the values in the formula $\rm A = P(1 + \dfrac{r}{100})^t$

The amount received after compounding at the end of 1 year will be:

$\rm A = 300(1 + \dfrac{5.5}{100})^1\\ \\ A=300(1.055)\\ \\ A=\ 316.5$

Similarly, the amount to be received after 2 years will be:

$316.5+316.5(1.055)$

The amount received after 10 years will be:

$316.5+316.5(1.055)+316.5(1.055)^2+.......$  upto 10 years

Therefore the summation that represents the money in account after 10 years is:

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

Learn more about compound interest here:

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