Question

solve no of years monthly payments =300 rate of interest = 12% Maturity value =8100 ​

Answer 1

ɪɴꜱᴛᴀʟᴍᴇɴᴛ ᴘᴇʀ ᴍᴏɴᴛʜ (ᴘ) = ʀꜱ. 300

ɴᴜᴍʙᴇʀ ᴏꜰ ᴍᴏɴᴛʜꜱ (ɴ) = ɴ

ʟᴇᴛ ʀᴀᴛᴇ ᴏꜰ ɪɴᴛᴇʀᴇꜱᴛ (ʀ) = 12%

Required formula :$\boxed{ \frak{ \red{Simple \: interest = Principal \times \frac{n \big(n + 1 \big)}{2 \times 12} \times \frac{r}{100} }}}$

$\sf{ {{Simple \: interest = Principal \times \frac{n \big(n + 1 \big)}{2 \times 12} \times \frac{r}{100} }}} \\ \\ \longmapsto \sf300 \times \frac{n(n + 1)}{2 \times 12} \times \frac{12}{100} \\ \\ \longmapsto \sf300 \times \frac{n(n + 1)}{24} \times \frac{12}{100} \\ \\ \longmapsto \sf \: n(n + 1) \times \frac{300 \times 12}{24 \times 100} \\ \\ \longmapsto \sf \: n(n + 1) \times \cancel \frac{3600}{2400} \\ \\ \longmapsto \sf n(n + 1) \times 1.5 \\ \\ \underline\blue{ \frak{ Rs.\:1.5n(n + 1)}} \:$

$\sf \: Maturity \: value = Rs. (300 \times n) +Rs.1.5n \\ \\ \sf= Rs.(300 + {1.5n}^{2} + 1.5)(n + 1)$

$\sf \: Given \: maturity \: value = Rs. 8,100$

$\sf \: then \: 300n + 1.5 {n}^{2} + 1.5 = 8100 \\ \\ \implies \sf1.5 {n}^{2} + 301.5n - 8100 = 0 \\ \\ \implies \sf {n}^{2} + 201n - 5400 = 0 \\ \\ \implies \sf(n + 225)(n - 24) = 0 \\ \\ \implies \sf = n - 225 \: \: \: or \: \: \: n = 24 \: months \:$

Then time 2 years