d Ao = 300, An+l = A,,-18 Using a rule to find the value of a simple interest lo
ID: 3147288 • Letter: D
Question
d Ao = 300, An+l = A,,-18 Using a rule to find the value of a simple interest loan or invest n years ment ah The value of a simple interest loan after n years, Vi, can be calculated from the rule Vn 8000512n. a What is the principal of this loan? b How much interest is charged every year in dollars? c Use the rule to find: 2 i the value of the loan after 12 years ii how long it takes for the initial investment to double. d Find the value of the loan after 15 years. The value of a simple interest investment after n years, Vn, can be calculated from the rule = 2000 + 70n. a What is the principal of this investment? b How much interest is charged every year in dollars? c Use the rule to find: 3 i the value of the investment after 6 years ii how long it takes for the initial investment to double. d Find the value of the loan after 10 years.Explanation / Answer
Vn = 8000 + 512n
At n=1
V1 = 8000 + 512 = 8512
At n=2
V2 = 8000 + 512*2 = 9024
Interest received from V1 to V2 = 9024 -8512 = 512
similarly V3 = 8000 + 512*3 = 9536
interest received from V2 to V3 = 9536 - 9024 = 512
a) The principle is clearly given as: 8000, because each year we can see that an interest of 512 is added to the principle. and after 1st year Vn = 8512, Interest = 512, principle = 8512 - 512 = 8000.
b) Simple interest = 512 = PRn/100
P = principle
R = rate
here, n=1
512 = PRn/100
512 = 8000*R*1/100
R/100 = 512/8000
R = 0.064*100 = 6.4%
c) i) value of loan after 12 years, n=12
V12 = 8000+512*12 = 8000+6144 = 14144
ii) for loan to double, Vn = 16000
16000 = 8000 + 512n
16000-8000 = 512n
n = 8000/512
n = 15.625 years
The loan will double in between 15 and 16 years.
d) value of loan after 15 years, n=15
V15 = 8000 + 512*15 = 8000 + 7680 = 15680
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