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Wize University Introduction to Finance Textbook > Time Value of Money

Lump Sum Calculations

Effective Rates with Continuous CompoundingPrevious Section
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Lump-Sum Calculations

  • A lump sum is a single amount at a specific point in time.
  • Lump-sum calculations involve finding the present or future value of single amounts.
  • Example: You have $5,000 today, what will this be worth in 7 years?
  • Finding the present value of some future value is called discounting.
  • Finding the future value of some present value is called compounding.

Wize Concept
The present value (PV) is inversely related to the discount rate (r). The future value (FV) is positively related to the discount rate (r).

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Example: Future Value of a Lump Sum

You deposit $1,000 into an account, earning 10% interest compounded annually.

a) How much will you have in your account in 3 years?
b) How long will it take for your money to grow to $2,000?
c) What interest rate would triple your money in 5 years?

Practice: Future Value of a Lump Sum

You deposit $4,000 today at the bank into your earning which earns 6% interest compounded monthly.

Round your answers to 2 decimal places.
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Example: Present Value of a Lump Sum

At the end of Year 2, Rabi will receive a $60,000 cheque from his father. At the end of Year 5, Rabi will receive a $35,000 cheque from his mother. The effective annual interest rate is 3.25%.

What is the total present value of Rabi’s cheques from his parents as of Year 0?
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Practice: Present Value of a Lump Sum

One night, Sean dreamed that a magic wizard offered him two gift options. The first gift option provides $1,000 in Year 2 and Year 4. The second gift option provides $950 in Year 1 and Year 3.

If Sean’s dream were to be true, which option should he select if the effective annual interest rate is 7.50%?
Extra Practice
Mark borrowed money January 1st, 2022. The term of the loan is 5 years at 6% interest per year. If the amount to be repaid in 5 years is $50,000 how much did Mark borrow if the loan is a pure-discount loan?
Tina took out a $20,000 pure-discount loan that matures in 7 years. The rate is 6%. How much will she repay at the end of 7 years?
You just borrowed $100,000 and agreed to repay the loan plus interest in 18 months. The loan carries a 5% interest rate compounded weekly.
How much will you repay at maturity?
Round your work to at least 6 decimal places and final answer to 2 decimal places.
You just invested $50,000 into an account earning 6% per year compounded weekly. You plan to make 3 more deposits of $20,000 each at the end of months 3, 8 and 15. How much will the investment be worth at the end of the two years?
Round your final answer to 2 decimal places.
You just enrolled in a new 5-year program at Harvard that will require 3 tuition payments of $50,000 each. The first payment is due today, the second payment is due at the end of your second year and the third payment is due at the end of your fifth year. The opportunity cost of your money is 6% per year.
What is the present value of your tuition?
Round your final answer to 2 decimal places.
You just received $12,000 from an investment you made 3 years ago. How much did you invest initially if you earned a return of 5% compounded monthly?
Round your final answer to 2 decimal places.
You just invested $10,000 into an account earnings 6% per year. How much will you have in your account 5 years from now?
Round your final answer to 2 decimal places.
Which of the following statements is true?
I. Ralph invested $3,500 in a bank offering 6% per year compounded once a year. After 4 years, he will have $4,418.67
II. Sarah promises to pay Mario $10,000 after 2 years. If the interest rate is 8% per year compounded once a year, Mario would give Sarah $8,357.33 now.
Tim invested $3000 in a bond that he expects to earn a 6% return per year. How much will the investment be worth after 10 years if Tim plans to sell the bond and retire?
Scott invested $5000 in a stock that he expects to earn a 10% return per year. How much will the investment be worth after 5 years?
John invested $1000 in a savings account that pays 3% interest per year. How much will the investment be worth after 5 years?
You just deposited $10,000 into a savings account that will earn 15% per year for the next 8 years and then 17% per year for the following 20 years. How much will you have in your account at the end of year 14?
How much should you invest today at 8% APR compounded weekly in order to have $50,000 in 10 years?