Question $1$: Interest Rates $[20$ Marks$]1\mathrm{.}1.$ Explain the following terms and statements: a$.$ Compounding $(2$ Marks$)$ b$.$ Discounting $(2$ Marks$)$ c$.$ Perpetuity $(2$ Marks$)$ d$.$ Annuity $(2$ Marks$)1\mathrm{.}2.$ John wants to borrow R$100000$ from First National Bank $($FNB$)$ to help his business. Suppose that FNB charges an interest rate of $8\%$ pr annum a$)$ If John wants to repay the loan after $1$ year, how much would he have to pay? $(2$ Marks$)$ b$)$ John hopes to get part of his inheritance from his aunt of R$70000$ in one $(1)$ years$$ time which he would use to repay part of the loan. In three years$$ time he plans to sell his sports car and use the proceeds to repay the rest of the loan. Calculate how much John will have to pay. $(4$ Marks$)$ c$)$ John hopes to repay the loan in $25$ years. He plans to use his house as collateral. Calculate the required annual repayments. $(3$ Marks$)$ d$)$ Calculate the effective annual rate FNB is charging in part c$.(3$ Marks$)$ include citation and reference list