Question $1$

NAD $1570$ is invested at $12\%$ p$.$a$.$ compound interest. After how many years will the investment be worth NAD$23000?$

$(10$ MARKS$)$

A farmer has just bought a new tractor for NAD$800000.$ He has to replace the tractor in $5$ years' time, when its trade$-$in value will be NAD$200000.$ The replacement cost of the tractor is expected to increase by $8\%$ per annum.

The farmer wants to replace his present tractor with a new one in $5$ years' time. The farmer wants to pay cash for the new tractor, after trading in his present tractor for NAD$200000.$ How much will he need to pay?

$(5$ MARKS$)$

One month after purchasing his present tractor, the farmer deposited $x$ NAD into an account that pays interest at the rate of $12\%$ p$.$a compounded monthly. He continued to deposit the same amount at the end of each month for a total of $60$ months. At the end of $60$ months, he has exactly the amount that is needed to purchase a new tractor, after he trades in his present tractor. Calculates the value of $x.$

$(5$ MARKS$)$

Suppose that $12$ months after the purchase of the present tractor and every $12$ months thereafter, he withdraws NAD$5000$ from his account, to pay for maintenance of the tractor. If he makes $5$ such withdrawals, what will the new monthly deposit be$?$

$(5$ MARKS$)$