Joseph the economist

Quantitative Finance Level 2

Joseph invests $ 6000 for 3 years at 4.5% simple interest in Simple Bank. The interest is paid, by cheque, at the end of each year. Joseph also invests $ 6000 for 3 years at 4.2% compound interest in Compound Bank. Which bank pays Joseph the greater amount of total interest?

Not enough data Simple Bank Both pay the same amount of total interest Compound Bank

2 solutions

Zyberg Nee
Apr 2, 2016

The formula for simple interest is: $F_s = P + P \times \frac{R}{100} \times t$

$F_s$ - Future value,
$P$ - Present value,
$R$ - The interest value per year,
$t$ - Time.

The formula for compound interest (when interest is counted every year) is: $F_c = P(1 + \frac{i}{100})^{t}$

$F_c$ - Future value,
$P$ - Present value,
$i$ - Nominal interest rate,
$t$ - Time.

In this case the present value is $\$6000$ , time is $3$ years and interest of simple bank $R = 4.5\%$ , interest of compound bank $i = 4.2\%$ . Let's add all those numbers to both formulas and solve them:

1) $F_s = 6000 + 6000 \times \frac{4.5}{100} \times 3 = 6810$

2) $F_c = 6000(1 + \frac{4.2}{100})^3 ≈ 6788.2$

We can easily see now that: $\boxed{F_s > F_c}$ .

Jase Jason
Mar 19, 2016

Too straightforward. 4.5% > 4.2%

Your answer may be right but your method is wrong. There is not much difference between 4.2% simple interest and 4.5% compound interest

Boss Agarwal - 2 years, 5 months ago

Joseph the economist

2 solutions

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