James lends a sum of money to his friend at interest such that the amo

Question

James lends a sum of money to his friend at interest such that the amount triples after 5 years when compounded annually. In how many years would the amount payable back become 9 times the sum loaned?

A. 7
B. 8
C. 9
D. 10
E. 11

firas92 · Answer

Let the amount loaned be  a  and rate of interest be  r  and  n  be the number of years the amount payable back would become 9 times the sum loaned

a(1+\frac{r}{100})^5=3a

1+\frac{r}{100}=\sqrt {3}

Now,  a(1+\frac{r}{100})^n=9a

(1+\frac{r}{100})^n=9

(\sqrt {3})^n=3^2

(3)^{\frac{n}{5}}=3^2

So,  \frac{n}{5}=2

n=10

Answer is  (D)

mohitmkkr · Answer

let the amount loaned be X
after 5 years-3x
after 10 years-9x

answer is- (d)

ScottTargetTestPrep · Answer

Since the amount triples after 5 years, it will triple again after another 5 years. In other words, it will become 3 x 3 = 9 times the original amount after 5 + 5 = 10 years.

If that was hard to see, let L be the amount loaned and let the annual rate be r percent; so that we have:

3L = L(1 + r/100)^5

(1 + r/100)^5 = 3

Now, we want to find n such that L(1 + r/100)^n = 9L. We have:

9L = L(1 + r/100)^n

(1 + r/100)^n = 3^2

(1 + r/100)^n =  ^2

(1 + r/100)^n = (1 + r/100)^10

Thus, n = 10.

Answer: D

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