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Financial mathematics, Study notes of Quantitative Techniques

National University of Science and Technology BulawayoQuantitative Techniques
Prof. Jayons Munetsi

its a good source to use very effective

Typology: Study notes

2023/2024

Uploaded on 10/28/2024

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NATIONAL UNIVERSITY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF INSURANCE AND ACTURIAL SCIENCE
QUANTITATIVE ANALYSIS OF BUSINESS
FINANCIAL MATHEMATICS
1. Find the present value of $500 due in 3 years at 8.5% p.a. compounded quarterly.
2. a) What amount of money accumulates to $10 000 over 5 years at 11% p.a. compounded
(i) semi-annually and (ii) quarterly?
b) Find the initial sum invested in each of the following compound interest cases:
i) the investment earns $1000 compound interest after 20 years at 12.25% p.a.
compounded semi-annually
ii) with compounding occurring monthly at 17.5% pa, investment earns $500 compound
interest after 2 years
3. How much money would you have to invest at 22.5% pa compounded half-yearly over
20 years to accumulate $1 000+000.
4. Suppose a present value of $500 is placed in a bank account paying interest of 6% p.a.
compounded weekly. If no money is withdrawn from the account, how long will it take
for the account balance to reach $700?
5. Find the compound interest for the following:
a) On $25.50 for 6 years at 4% compounded annually
b) On $20 for 15 years at 2.5% compounded half-yearly
c) On $1000 for 10 years at 12% compounded monthly
d) On $5000 for 5 years compounded quarterly
6. An investment is made at an initial cost of $50+000. It returns $15+000 after 1 year and
$45+000 after two years and then has no further returns. What is the rate of return for
this investment?
7. Suppose that a person has the following choices of investing $10+000:
a) Placing the money in a savings account paying 6% compounded semi-annually;
b) Investing in a business such that the value of investment after 8ywears is $16+000.
Which is a better option?
8. Sam a 20 year old graduate has just found his first full-time job. An investment analyst
suggests that he should try to have a substantial amount saved by the time of his planned
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NATIONAL UNIVERSITY OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF INSURANCE AND ACTURIAL SCIENCE

QUANTITATIVE ANALYSIS OF BUSINESS

FINANCIAL MATHEMATICS

  1. Find the present value of $500 due in 3 years at 8.5% p.a. compounded quarterly.
  2. a) What amount of money accumulates to $10 000 over 5 years at 11% p.a. compounded (i) semi-annually and (ii) quarterly? b) Find the initial sum invested in each of the following compound interest cases: i) the investment earns $1000 compound interest after 20 years at 12.25% p.a. compounded semi-annually ii) with compounding occurring monthly at 17.5% pa, investment earns $500 compound interest after 2 years
  3. How much money would you have to invest at 22.5% pa compounded half-yearly over 20 years to accumulate $1 000 000.
  4. Suppose a present value of $500 is placed in a bank account paying interest of 6% p.a. compounded weekly. If no money is withdrawn from the account, how long will it take for the account balance to reach $700?
  5. Find the compound interest for the following: a) On $25.50 for 6 years at 4% compounded annually b) On $20 for 15 years at 2.5% compounded half-yearly c) On $1000 for 10 years at 12% compounded monthly d) On $5000 for 5 years compounded quarterly
  6. An investment is made at an initial cost of $50 000. It returns $15 000 after 1 year and $45 000 after two years and then has no further returns. What is the rate of return for this investment?
  7. Suppose that a person has the following choices of investing $10 000: a) Placing the money in a savings account paying 6% compounded semi-annually; b) Investing in a business such that the value of investment after 8ywears is $16 000. Which is a better option?
  8. Sam a 20 year old graduate has just found his first full-time job. An investment analyst suggests that he should try to have a substantial amount saved by the time of his planned

retirement on his 65th^ birthday. The analyst presents comparisons between two saving plans. Plan A: Sam should invest $5000 on his 21st^ birthday then $2 000 0n each birthday up to and including his 31.No further deposits are made but the money invested continues to earn interest until his 65 birthday. Plan B : Sam should make the first deposit of $5 000 on his 31 birthday then continue to deposit $2 000 per birthday with the last deposit being made on his 65 birthday. If the effect annual rate of interest is 7.5% p.a., how much should Sam have in savings at age 65 under each plan? Assume all the contributions are made at the end of the year

  1. Phuc is evaluation two possible projects Project A runs for 10 years. It involves spending $10 000 immediately, but returns an equal amount of $2 000 at the beginning of every 6 months. The interest rate is 10% p.a. compounded semi-annually for the whole ten years. Project B runs for 10 years. It involves spending $7 000 immediately, but returns $1 400 at the end of each year for the next 10 years. The interest rate is 8% p.a. compounded annually for the first 6years and 4% p.a. compounded annually for the last 4years. Assume the Phuc can only choose 1 project, which project should Phuc invest in?
  2. Find the length of time required for the following investments to yield their respective compound values a) $500 to amount to $50 000 at 4.75% compounded yearly b) $1000 to amount to $2500 at 8% compounded half-yearly c) $12 000 to amount to $24000 at 10% compounded quarterly d) $888 to amount to $16 000 at 16% compounded monthly
  3. What weekly payment would be required to exhaust a $500 000 annuity paying 18% over 5 years.
  4. Mr. Moyo is financing $69 700 for a home at 7% interest with a 20-year fixed-rate loan. Find the interest paid and principal paid for each of the first 5 months of the loan and find the principal owed at the end of the 5th^ months.
  5. Charity has made a $500 000 business loan. Her 10-year fixed-rate loan has an interest rate of 8.5%. Create an amortization schedule.

Annuity Due A 5000 2 9 B 12000 5 7. C 25000 10 8 D 8000 3 13 E 15000 7 10 F 35000 4 9.

  1. Payments of $400 are made at the end of each quarter into an account earning 4.8% annual interest compounded quarterly. What is the future value of the account at the end of 5 years?
  2. At the end of each month, payments of $200 are made into an account earning 6.2% annual interest compounded monthly. Find the future value of the account at the end of 10 years.
  3. Find the PV of an annuity that pays $4000 at the end of each quarter for 10 years if the annual interest rate is 5.5% compounded quarterly.
  4. What is the PV of an annuity that pays $1500 at the end of each month for 10 years if the annual interest rate is 7.5% compounded monthly?
  5. Payments of $250 are made at the end of each quarter into an account that earns 6% interest compounded quarterly. Find the value of the account in 5 years.