How many years would it take for $25000 to become $1000000 at 5 percent annual interest compounded quarterly?
1000000 = 25000 (1+ 5/400)^(4t)
40 = (405/400)^(4t)
40 = (1.0125)^(4t)
Taking log to both sides we get
log 40 = log (1.0125)^(4t)
log 4 + log 10 = 4t log 1.0125
log 2^2 + 1 = 4t (0.00539)
0.602 + 1 = 0.02156t
t = 1.602/0.02156
t = 74.3 years
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A = p(1 + r/n)^nt
1,000,000 = 25,000(1 + 0.04/4)^4t
40 = (1.01)^4t
ln40 = 4tln1.01
3.689 = 4(0.00995)t
3.689 = 0.0398t
t = 3.689/0.0398 = 92.7 years
check:
40 = (1.01)^4(92.7)
40 = 40 checks
5% compounded quarterly is 1.25% per quarter.
25000(1.0125)^k = 1000000
1.0125^k = 40
k ln (1.0125) = ln 40
k = ln 40 / ln (1.0125)
k =approx.= 297 quarters
297 quarters = 74.25 years
Comments
1000000 = 25000 (1+ 5/400)^(4t)
40 = (405/400)^(4t)
40 = (1.0125)^(4t)
Taking log to both sides we get
log 40 = log (1.0125)^(4t)
log 4 + log 10 = 4t log 1.0125
log 2^2 + 1 = 4t (0.00539)
0.602 + 1 = 0.02156t
t = 1.602/0.02156
t = 74.3 years
I am a math tutor for the new app MathCrunch. You should download MathCrunch for free on your phone to get instant math help anytime anywhere!
A = p(1 + r/n)^nt
1,000,000 = 25,000(1 + 0.04/4)^4t
40 = (1.01)^4t
ln40 = 4tln1.01
3.689 = 4(0.00995)t
3.689 = 0.0398t
t = 3.689/0.0398 = 92.7 years
check:
40 = (1.01)^4(92.7)
40 = 40 checks
5% compounded quarterly is 1.25% per quarter.
25000(1.0125)^k = 1000000
1.0125^k = 40
k ln (1.0125) = ln 40
k = ln 40 / ln (1.0125)
k =approx.= 297 quarters
297 quarters = 74.25 years