📝 Chapter 6: Financial Mathematics

\$3000 invested at 4.5% per year compounded annually for 7 years. Find the final amount.

How much should be deposited today at 5% compounded semi-annually to grow to \$8000 in 6 years?

FV of an ordinary annuity: \$300 deposited at the end of each month for 4 years at 6% compounded monthly.

PV of an ordinary annuity: \$1000 paid at the end of each year for 8 years at 4% compounded annually.

A loan of \$15{,}000 at 6% per year compounded monthly is amortised over 4 years. Find the monthly payment.

A young professional starts saving \$200/month at age 25 for 40 years at 7% compounded monthly. Find the future value at age 65, then determine how much would have to be saved monthly starting at age 35 to achieve the same total.

An annuity pays \$2000 every 6 months for 10 years. The present value at 8% compounded semi-annually is what amount? Round to the nearest dollar.

A \$200{,}000 mortgage at 4% per year compounded semi-annually is amortised over 25 years (monthly payments). (a) Find the equivalent monthly rate \( i_{\text{mo}} \) such that \( (1 + i_{\text{mo}})^{12} = (1.02)^2 \). (b) Find the monthly payment.

Explain the difference between FV and PV of an annuity. Use a real-world example for each (e.g. a savings goal vs. a loan or pension).

Why is the FV of an ordinary annuity formula a finite geometric series in disguise? Show the connection.

In an amortisation schedule, why does the proportion of each payment going to interest decrease over time? Use a 30-year mortgage as your context.

A teen says, "Saving \$50/month is the same as saving \$600 once a year." Use the language of FV-of-annuity to explain why this is not quite true if the account compounds monthly.

Mei is saving for a down payment of \$30{,}000 in 5 years. The bank pays 3% compounded monthly. (a) How much should she save at the end of each month? (b) What is the total amount she will deposit? (c) How much interest is earned?

A retiree receives \$3000/month for 20 years from a fund earning 5% per year compounded monthly. (a) What lump sum was needed at retirement? (b) What is the total of all payments received? (c) How much of that total is interest?

Compare two student-loan options for \$20{,}000: (Option A) 5%/year, 6 years; (Option B) 6%/year, 4 years. Both compounded monthly. (a) Find the monthly payment for each. (b) Find the total interest for each. (c) Which is cheaper overall? Justify.