Question

For an investment of $100,000 at 5% interest for 8 years, find (a) the simple interest & (b) the compound interest if interest is calculated once per year.

Answer 1

1) Simple Interest

	$
Principal amount	100000
Interest Rate	0.05
Tenure of loan	8 years
Formula for simple interest
=Principal*rate of interest*tenure
=100,000*5%*8
=40000
$40,000 will be the amount of interest that will be given for the entire period of loan .
so 1st year interest that will be paid ( as interest in this question is calculated annually)
100000*5%*1
5000

2) Compound Interest:

In compound interest, interest is paid on principal as well as on interest earned every calculation

Year	Principal/opening balance	Interest 5% compounded annually	closing balance(opening balance +interest of that year)
1	100,000	5,000(100,000*5%*1)	105,000
2	105,000	5,250(105,000*5%*1)	110,250
3	110,250	5,513(110,250*5%*1)	115,763
4	115,763	5,788(115,763*5%*1)	121,551
5	121,551	6,078(121,551*5%*1)	127,628
6	127,628	6,381(127,628*5%*1)	134,010
7	134,010	6,700(134,010*5%*1)	140,710
8	140,710	7,036(140,710*5%*1)	147,746

therefore closing balance including principal and total interest earned by the end of year8= $147,746

Prinicial = $100,000

amount or closing bal= $147,746

interest for 8 years= 147746-100000=$47,746

or interest= 5000+5250+5513+5788+6078+6381+6700+7036= $47,746

formula for compound interest=

amount=principal(1+r/n)nt

r= rate of interest

n= no. of times interest is compounded in a year

t= tenure

Amount=100,000(1+(5%/1))1*8

=147,746

compound interest= amount-principal= 147746-100000=$47,746