Answer to Question #306618 in Financial Math for Ndi

Question #306618

If 35 000 accumulates to 48 328 at a continuous compounded rate of year then the term under consideration is


1
Expert's answer
2022-03-08T13:33:02-0500

Solution


Using the Formula


A=PertA=Pe^{rt}


Here AA is the amount accumulated, PP is the principal amount invested, rr is the interest rate and tt is the tenure.


Therefore, we can write,


48328=35000(ert)48328=35000(e^{rt})


ert=4832835000e^{rt}=\frac{48328}{35000}


ert=1.3808e^{rt}=1.3808


ln(ert)=ln(1.3808)ln(e^{rt})=ln(1.3808)


rt×ln(e)=ln(1.3808)rt\times ln(e)=ln(1.3808)


rt×(1)=ln(1.3808)rt\times (1)=ln(1.3808)


t=ln(1.3808)rt=\frac{ln(1.3808)}{r}


Therefore, knowing the value of rr, we can find the tenure.


For example if r=6.8%r=6.8\%


Then


t=ln(1.3808)6.8%t=\frac{ln(1.3808)}{6.8\%}


t=ln(1.3808)0.068t=\frac{ln(1.3808)}{0.068}


t=4.745t=4.745  years




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