Finance (29/05/26) (Mathematics)

Pfuture =

Ppresent (1 + r/100)ⁿ

• population growth

effect/nominal rate:

how does n change in three different situations?

Payment at the beginning of the period: use n − 1

Payment at the end of the period: use n

Payment one period later than normal: use n + 1

annuity ~

a plan taking regular payments for lump sum/ investment

what to do if ‘on the day’ / ‘immediately’?

n + 1

what to do if it sits in bank or ‘last payment early’?

multiply by (1 + i)ⁿ

how to get interest paid?

Total Interest Paid = Total Payments - Principal Borrowed

* Total Payments = Payment Amount × Number of Payments

when to use Pv? (3)

loans/bond, retirement (at retirements to see series of payments), withdrawals from sum of money,

when to use Fv? (2)

savings, retirement (before retirement when saving), sinking fund

what to do if loan taken and payment made at same time?

P must be subtracted from an original loan (seen as deposit

Outstanding balance =

A - Fv

What to do if there is an investment before?

add to formula

eg. investment + Fv

how does n work for effective rate?

normal none of this monthly business

Outstanding Balance =

how to get amount owed once you can pay?

1. Find how much interest was gained when you didn’t pay (compound)

2. Set ANS equal to Pv (n is installment number after OB)

3. Find unknowns

P ~

amount of loan taken

how to get ‘value of last payment’?

get OB

what to do when looking to trade-in?

original w/ interest - original w/ depreciation

what to remember?

dont round up even for payments or year

when doing outstanding balance, what to remember?

remember to subtract by price to pay off with compound interests loan

What to remember when solving for years or just n

Round up

Balance outstanding =

(Orignal loan to future date) - (Fv of payments made so far)

What to remember if using shares?

To get profit use the Fv - cost of shares

What does n in Fv and Pv give?

• The number of months (payments depending on question but if monthly its just months)

• Only need to fivide by 12 if they want the answer in years