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Grade 11 Maths question

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Grade 11 Maths question

LinkTainted

Member
Sep 29, 2019
9
1
Can someone please elaborate this question please:

A savings scheme is offering a rare of of 3.5% per year for the lifetime of the plan. Mike wants to save up to $20000. He works out that he can afford to save $500 every year, which he will deposit on 1 January. If interest is paid on 31 December, how many years will it be before he has saved up his $20000?
 

Ezekiel

Active member
Editor
Sep 9, 2019
32
12
All you need to do to solve the question is:

500 [s x] = 20,000, where [s x] represents this accumulation at 3.5% over x years (so you're solving for this x), remembering that [s x] is the value at the beginning of the particular year, so after that year's $500 has been saved but before any interest for that year has been added (see https://www.thecalculatorsite.com/ar...ue-formula.php for a reminder of the calculation).

From my (ancient, = 1952!) 3.5% actuarial tables [s 25] = 38.9499, and [s 26] = 41.3131, so at some point in that 25th year he'd actually already have enough without adding the £500 at the beginning of year 26. So the answer is 25 years plus the number of days it takes 500*38.9499 = $19,474.95 to accumulate to $20,000 at 3.5% per year interest, assuming interest can be taken mid-year on request, or 26 years if it can't be taken mid-year.
 

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