Question

Bill Baxter has 25000 to invest for a year he can lend it to his sister who has agreed to pay 10% simple interest for the year or he can invest it with a bank at 6 copunded quartly for a year how much additional interest would the simple interest loan to his sister generate find the effective interest rate for both payment

Answer 1

When he lend it to her sister;

Interest, $I=\frac{P\times R \times T}{100}=\frac{2500\times 10 \times 1 }{100}=2500$

When he lend it to the bank;

$r=6\%/4=1.5\%, n=1\times 4=4, P =25000$

$A=P(1+r/100)^n=25000(1+1.5/100)^4=26534.09$

Interest earned= A-P=26534.09-25000=1534.09

Additional interest earned =2500-1534.09=965.91

Calculation for effective interest rate:

Effective interest rate, r = $(1+i/n)^n -1$

For the sister $r=(1+0.1/4)^4-1=0.1038=10.38\%$

For the bank $r=(1+0.06/1)^1-1=0.06=6\%$