Question

Mrs smith invests R25000,00 in an account earning 7,5% interest per year,compounded weekly. After a number of years, she receives double the amount she invested. Determine the period under consideration. Round your answer to the nearest year

Answer 1

50000$=$ 25000$[$ 1$+$$\frac{0.075}{52}$ $]$ $^{52t}$

$\frac{50000}{25000}$ $=$ $\frac{25000}{25000}$ $[$ 1.00144$]$ $^{52t}$

2$=$ $[$ 1.001442$]$ $^{52t}$

Log 2 $=$ log $[$ 1.001442$]$ $^{52t}$

Log 2 $=$ $($ 52t$)$ $[$ log 1.001442$]$

$\frac{0.3010299}{0.00624}$ $=$ 52t

482.37$=$ 52t

$\frac{482.37}{52}$ $=$ 9.27

Answer: more than 9 years.