Comparing savings offers

Comparing savings offers

Secondary 4
9 marks
TGM Original Questions

A saver deposits $6000 for exactly four years. Two fictional offers are shown. There are no withdrawals or further deposits. Interest is calculated using the unrounded balance; no intermediate amount is rounded. Round only each requested final monetary answer to the nearest cent.

Offer AOffer B
2.8% compound interest per year. Interest is credited at each year-end. No fees or bonus.3% interest is credited at each year-end, then a $15 fee is deducted. This happens in each of the four years. After the fourth fee, a one-off $60 bonus is added. No other fees.
  1. Calculate the final balance under A.[2]
  2. Calculate the final balance under B, showing the balance after each annual fee.[3]
  3. Suppose only B’s terminal bonus is changed, with all other terms fixed. Find the smallest whole-dollar bonus that makes B’s final balance exceed A’s by at least 1% of the original $6000 deposit. Show that your bonus meets the requirement and the next smaller whole-dollar bonus does not.[3]
  4. Compare the original advertised offers, with B’s $60 bonus. Recommend an offer for this saver, giving a reason.[1]

Solution:

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Answer:(a) \(\$6700.75\). (b) \(\$6750.30\). (c) Minimum whole-dollar bonus \(\$71\); \(\$70\) fails. (d) Original offer B.

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