Question

Calculate the future value of $51,123.21, earning interest at a rate of that is compounded daily for 20 years and 2 months (use the traditional Banker’s rule of 30 days per month).

Answer 1

To calculate the future value of $51,123.21 earning compounded daily interest for 20 years and 2 months, you need to use the formula for future value. However, the interest rate is not provided in the question, so the exact future value cannot be calculated without it.

Step-by-step explanation:

To calculate the future value of $51,123.21 with compounded daily interest, we need to use the formula:

Future Value = Principal × (1 + (interest rate/compounding periods))^number of compounding periods

In this case, the principal is $51,123.21, the interest rate is not provided, the compounding period is daily, and the number of compounding periods is calculated based on 20 years and 2 months.

First, we need to convert 20 years and 2 months into the number of days. Since the Banker's rule considers 30 days per month, we have:

20 years = 20 × 365 days

2 months = 2 × 30 days

Now, we can calculate the total number of days:

Total number of days = 20 × 365 + 2 × 30 = 7,330 days

Using the formula, the future value can be calculated as:

Future Value = $51,123.21 × (1 + (interest rate/365))^7,330

Please provide the interest rate to get the exact future value.

Answer 2

The compound interest formula is :
`A = P(1+ (r)/(n))^n ^t`

where, A= Future value including the interest,

P= Principle amount, r= rate of interest in decimal form,

t= number of years and n= number of compounding in a year

Here, in this problem P= $ 51,123.21 , t= 20 years and 2 months

So, t= 20 + (2/12) years

t= 20 + 0.17 = 20.17 years

As the amount is compounded daily, so n= (12×30)= 360 [Using the traditional Banker’s rule of 30 days per month]

Thus,
`A = 51,123.21( 1+ (r)/(360))^3^6^0^*^2^0^.^1^7`

`A= 51,123.21 (1+(r)/(360))^7^2^6^1^.^2`

When the interest rate is given, then we can use this equation for finding the future value.