Future Value Suppose 10,000 is invested at an annual rate...

Future Value Suppose $\$ 10,000$ is invested at an annual rate of $5 \%$ for 10 yr. Find the future value if interest is compounded as follows.
(a) annually
(b) quarterly
(c) monthly
(d) daily ( 365 days)

Key Concepts

Compound Interest

Compound interest refers to the process of earning interest not only on the initial principal but also on the accumulated interest from previous periods. This exponential growth mechanism means that each interest calculation adds more to the balance, leading to increasing returns over time.

Future Value

Future value is the amount of money an investment will grow to over a period of time at a specific interest rate, taking into account the effect of interest compounding on a principal amount. It reflects how much an initial sum will be worth at a future date provided that the rate of return remains constant and that earnings are reinvested.

Compounding Frequency

Compounding frequency involves how often interest is calculated and added to the principal over a given period. More frequent compounding, such as quarterly, monthly, or daily, results in a higher effective rate and greater future value because interest is being applied and reinvested more often within each period.

Transcript

00:01 In this problem of exponential function, we have given that suppose $10 ,000 is invested, so this is the amount that is invested, that is $10 ,000 is invested at a rate of here 5%.

00:16 So this is rate 5 % or we can say this is 0 .05 for 10 years.

00:21 So the tenure is here 10 years.

00:24 Find the future value if interest is compounded.

00:28 In the first case, interest is compounded.

00:29 In the first case, interest is compounded annually so this is annually in the second case the interest rate is compounded quarterly in the third case the interest rate is compounded monthly and in the fourth case it is compounded daily that is 365 days so now we have the formula this is the p this is the rate and this is a time t and we when annually n is equal to 1 and we have the formula that is amount is equal to p 1 plus r divide with n.

01:13 So this would be n is equal to 1.

01:16 So this would be simply r.

01:17 So this would be r to the power t because we have t equals to 10 and now we have to calculate.

01:25 So this would be 10 ,000 multiplied with 1 plus 0 .05.

01:31 Now multiply it with this the power is 10 and now solve it.

01:35 So this would be equal to this is equals to 16 ,000, this is equal to 16 ,288 .9 .4.

01:48 So this is the amount.

01:50 And now in the second case, we have n is equal to this is here quarterly, so that means n equals to 4.

01:56 And now amount would be a equals to p...