2.2. Tom and Jerry are arguing about interest on money that they have given them for Christmas. They each received R2 345, Tom wants to invest his money at Old Mutual for 7 years at a compound interest rate of $$ 19.9 \% $$ per annum, while Jerry claims he will do better at Assupol earning $$ 23.41 \% $$ simple interest per annum over 7 years. Who is correct? ?

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**Step 1. Calculate Tom’s Final Amount with Compound Interest**

Tom invests at a rate of $$ 19.9\% $$ per annum (i.e., $$ r = 0.199 $$) on an initial amount $$ P = 2345 $$ over $$ t = 7 $$ years. The compound interest formula is

$$
A = P(1+r)^t
$$

Substitute the values:

$$
A = 2345(1+0.199)^7 = 2345(1.199)^7
$$

Calculating $$ (1.199)^7 $$ approximately gives:

$$
(1.199)^7 \approx 3.567
$$

Thus, Tom’s final amount is approximately:

$$
A \approx 2345 \times 3.567 \approx 8367
$$

**Step 2. Calculate Jerry’s Final Amount with Simple Interest**

Jerry invests at a simple interest rate of $$ 23.41\% $$ per annum (i.e., $$ r = 0.2341 $$) on the same principal $$ P = 2345 $$ over $$ t = 7 $$ years. The simple interest formula is

$$
A = P(1 + r \times t)
$$

Substitute the values:

$$
A = 2345\left(1 + 0.2341 \times 7\right)
$$

Calculate the interest factor:

$$
0.2341 \times 7 \approx 1.6387
$$

Thus,

$$
A \approx 2345 \times (1 + 1.6387) = 2345 \times 2.6387 \approx 6188
$$

**Step 3. Compare the Two Final Amounts**

- Tom’s final amount at Old Mutual (compound interest) is approximately $$ \pounds8367 $$.
- Jerry’s final amount at Assupol (simple interest) is approximately $$ \pounds6188 $$.

Since

$$
8367 > 6188,
$$

Tom’s investment yields a higher final amount.

**Conclusion:** Tom is correct.
Tom is correct because his investment with compound interest at 19.9% over 7 years yields more than Jerry's simple interest investment at 23.41% over the same period.

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