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Part 1

Value of a single amount versus a mixed stream  Personal finance problem   Gina Vitale has just contracted to sell a small parcel of land that she inherited a few years ago. The buyer is willing to pay

​$26 comma 492

​now, or the buyer will make a series of payments starting now and continuing at annual intervals shown in the following​ table,

LOADING...

. 

Because Gina​ doesn't really need the money​ today, she plans to let it accumulate in an account that earns

7

​% 

annual interest. Given her desire to buy a house five years after selling the​ lot, she decides to choose the payment

alternativelong dash

either 

the lump sum or the mixed

streamlong dash

that 

provides the higher future value at the end of 5 years. Which alternative will she​ choose?

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Part 1

The future​ value,

FV Subscript n

​, 

of the lump sum deposit is

​$enter your response here

. 

​(Round to the nearest​ cent.)

To help Gina determine which alternative to choose, we need to compare the future value (FV) of the lump sum and the mixed stream of payments at the end of 5 years, given the 7% annual interest rate.

### **Step 1: Future Value of the Lump Sum**

The formula for the future value of a lump sum is:

\[
FV = PV \times (1 + r)^n
\]

Where:
- $ PV $ = present value or initial lump sum
- $ r $ = interest rate per period (annual rate in this case)
- $ n $ = number of periods (5 years)

Given:
- $ PV = 26,492 $
- $ r = 7\% = 0.07 $
- $ n = 5 $

Substitute the values into the formula:

\[
FV = 26,492 \times (1 + 0.07)^5
\]

Let me calculate this for you.The future value (FV) of the lump sum at the end of 5 years is approximately **$37,156.40**.

Next, we need to calculate the future value of the mixed stream of payments. Do you have the details of those payments, or would you like to proceed with this part? 

Here are 5 related questions:
1. What is the schedule of payments for the mixed stream?
2. How do we calculate the future value for each payment in a stream?
3. What is the importance of the interest rate in future value calculations?
4. How does compound interest affect the growth of a lump sum versus multiple payments?
5. What assumptions are made about the interest rate staying constant over 5 years?

**Tip:** Future value of a mixed stream requires calculating the future value of each individual payment.

Gina Vitale has just contracted to sell a small parcel of land and is choosing between receiving a lump sum of $26,492 now or a mixed stream of payments starting now. She plans to deposit the money into an account earning 7% annual interest and will use it to buy a house in 5 years. Which option provides the higher future value at the end of 5 years?

Learn how to calculate the future value of a lump sum vs. a mixed stream of payments, given a 7% interest rate over 5 years. This example explores the compound interest formula and future value of cash flow streams, helping you choose the best option. Suitable for personal finance and investment students.

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