Math problem?

Question

You invest $1000 for ten years. Determine the total interest earned if the investment earns 8% per annum.

a. compounded annually
b. compounded semi-annually

Answer 1

The formula is A= P(1+ r/k)^kt where
P is the amount after interest
A is the principle (amount before interest)
r is the interest rate (0.08)
k is the # of times it is compounded (a-1, b-2)
t is the time (in years, so it would be 10)

a) A= 1000 * (1+ 0.08)^10
A= 1000 * 1.08^10
A= 1000 * 2.158924997
A= 2158.92
You have $2158.92 after 10 years compounded annually, meaning you earned $1158.92 interest.

a) A= 1000 * (1+ 0.08/2)^2*10
A= 1000 * 1.04^20
A= 1000 * 2.191123143
A= 2191.12
You have $2191.12 after 10 years compounded semi-annually, meaning you earned $1191.12 interest.

Answer 2

Principal = $ 1000 , Time = 10 yrs, Rate of interest = 8% per annum. Formulae for calculating the interest are as follows.

(I) Amount due (A) after given time (t yrs) = [ 1 + (R/ 100n) ]^n, where n = 1 for annual compounding and = 2 for semi-annual compounding.

(II) Interest earned = Amount - Principal
Using these two foemulae you get your answers.

(a) A = 1000 [ 1 + ( 8 / 1 x 100 ) ]^1 = $ 1080
Hence Interest earned = 1080 - 1000 = $ 80

(b) A = 1000 [ 1 + ( 8/2x100 ) ]^2 = $ 1081. 6
Hence Interest earned = 1081.6 - 1000 = $ 81.60

Answer 3

The general formula is where I=Interest, P=Principal, n=number of periods, and r=rate is:

I = (P(1+r)^n)-1

In problem (a), P=$1000, n=10, and r=8%.
So I = ($1,000(1.08)^10) - $1,000 = $2,158.93 - $1,000= $1,158.93. In other words, you'd have a total of $2,158.93 at the end of ten years, of which $1,158.93 would be interest.

In problem (b), P=$1000, n=20, and r=4%.
So I = ($1,000(1.04)^20) - $1,000 = $2,191.12 - $1,000= $1,191.12. In other words, you'd have a total of $2,191.12 at the end of ten years, of which $1,191.12 would be interest.

You can see that by compounding semi-annually instead of annually, you'd earn an extra $32.20.

Answer 4

open calculator
enter 1000
*
1.08
hit enter button 10 times
now subtract 1000
= annually

enter 1000
*
1.04
hit enter button 20 times
now subtract 1000
= semiannually

all the best

Answer 5

Answers above gave result of how much you would have. Questions was how much interest was earned. Subtract original $1000

A) $1,158.92
B) $1,191.12

Answer 6

I = 1000 ( 1 + (0.08/1))^10
a) apprx. $2158.92 final amount after ten years

I = 1000 ( 1 + (0.08/2))^20
b) apprx. $2191.12 final amount after ten years

Answer 7

a. 1000*1.08^10 = 2158.925 = $2158.93
b. 1000*1.08^20 = 4 660.95714 = $4660.96

Answer 8

I think youll find its called Maths Dear Boy..........

Well 8 percent of that over a year (Annually) would be $80 and half a year (semi annually) would be $40 what what.........

Answer 9

Go to www.getobjects.com/Components/Finance/TVM/iy.html and it will explain it all for you. They're easy answers, but go the site, so you could learn how to do it.

Answer 10

A.} $80
B.}$40