Answer to Question #311095 in Financial Math for tumi

Question

Sbusiso needs R150 000 on 17 November 2022 to upgrade his restaurant. On 8 January 2022 he deposited an amount into an account earning 13,45% interest per year, compounded monthly, and being credited on the 1st of every month. If fractional compounding is used for the full term, then the amount that Sbusiso deposited on 8 January 2022 was

Answer 1

According to the compound interest formula

$R=P(1+{\frac i n})^{t*n}\implies P={\frac R {(1+{\frac i n})^{t*n}}}$ , where P - initial value, i - yearly interest, n - number of payments in one year, t - number of years

So, in the given case

$P={\frac {150000} {(1+ {\frac {0.1345} {12}})^{{\frac 9 {12}}*12}}}={\frac {150000} {1.0112^9}}\approx135694$