Annuities and loans
Planning to a savings goal
Turn a goal into a plan: solve for the monthly saving, the time needed or the return required, and set the target in today's riyals.
Learning objectives
- Solve for the regular saving needed to reach a target, allowing for money already saved
- Solve for the time needed (NPER) and the return required (RATE) when the saving is fixed
- Apply the spreadsheet sign convention so the functions return sensible answers
- Restate a goal set in today's riyals as a future target before planning
A savings goal has five moving parts: the target, the time until you need it, what you have already saved, what you add each period, and the return the money earns. Fix any four and the fifth is determined. Financial planners, bank advisers and anyone building a household budget solve this problem constantly, usually by asking one of three questions:
- How much must I save each month? (solve for the payment)
- How long will it take at what I can afford? (solve for time)
- What return would I need? (solve for the rate, and then ask whether that return is realistic)
It is the annuity from earlier lessons run forwards: instead of the present value of a stream of payments, you want its future value.
FV = S × (1 + r)ⁿ + PMT × [(1 + r)ⁿ − 1] ÷ r
- S
- amount already saved today
- PMT
- saving added at the end of each period
- r
- return per period (annual rate ÷ 12 for monthly saving)
- n
- number of periods until the goal
Included with a Formula Quest membership
The rest of this lesson is for members. Members get the full lesson, including its 3 graded exercises, and every other Finance Quest lesson.