Question

Ivan put 500 000ISK (Icelandic Krona) and Blake put 700 000ISK into savings accounts

Answer 1

Using compound interest, it is found that Blake receives an annual rate of 4.27%.

Compound interest:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

• A(t) is the amount of money after t years.  
• P is the principal(the initial sum of money).  
• r is the interest rate(as a decimal value).  
• n is the number of times that interest is compounded per year.  
• t is the time in years for which the money is invested or borrowed.

Ivan's parameters are given by:

• Put 500 000 ISK, hence $P = 500000$
• 8 years, hence $t = 8$
• Quarterly compounding, hence $n = 4$
• Interest rate of r.

Hence:

$A_i(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

$A_i(t) = 500000\left(1 + \frac{r}{4}\right)^{32}$

$A_i(t) = 500000(1 + 0.25r)^{32}$

Blake's parameters are given by:

• Put 700 000 ISK, hence $P = 700000$
• 8 years, hence $t = 8$
• Quarterly compounding, hence $n = 4$
• Interest rate that is half of Ivan's, hence $\frac{r}{2}$

Thus:

$A_b(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

$A_b(t) = 700000(1 + 0.125r)^{32}$

These amounts are equal, hence:

$A_i(t) = A_b(t)$

$500000(1 + 0.25r)^{32} = 700000(1 + 0.125r)^{32}$

$\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32} = \frac{700000}{500000}$

$\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32} = \frac{7}{5}$

$\sqrt[32]{\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32}} = \sqrt[32]{\frac{7}{5}}$

$\frac{1 + 0.25r}{1 + 0.125r} = \left(\frac{7}{5}\right)^{\frac{1}{32}}$

$\frac{1 + 0.25r}{1 + 0.125r} = 1.01057023172$

$1 + 0.25r = 1.01057023172 + 0.12632127896r$

$0.12367872103r = 0.01057023172$

$r = \frac{0.01057023172}{0.12367872103}$

$r = 0.0854$

Blake's rate is:

$\frac{r}{2} = \frac{0.0855}{2} = 0.0427$

Blake receives an annual rate of 4.27%.

A similar problem is given at brainly.com/question/24507395