Chapter 7.7, Problem 2STP

For Exercises $1-5,$ choose the correct letter.

Suppose you deposit $500 into an account earning $7.8\%$ interest compounded annually. How long will it take for the account to be worth $1000?

F. between 6 and 7 years

H. between 8 and 9 years

G. between 7 and 8 years

I. between 9 and 10 years

To determine

To calculate: Suppose you deposited $500 into an account earning 7.8% interest compounded annually. How long will it take for the account to be worth $1000?

F. between 6 and 7years

H. between 8 and 9years

G. between 7 and 8 years

I. between 9 and 10 years

Answer to Problem 2STP

option I is correct

Explanation of Solution

Given information: principal = $500, interest rate = 7.8% and Final Amount = $1000

Calculation: money is Compounded annually, so we use the formula $A=P{\left(1+\frac{r}{100}\right)}^t$ where A = Final amount

P = Principal amount

  $r$ = rate of interest

  $t$ = time (in years)

so, $1000=500{\left(1+\frac{7.8}{100}\right)}^t$

  $2={\left(1+\frac{7.8}{100}\right)}^t$

Taking log both sides, we get

  $\log 2=t*\log \left(1+\frac{7.8}{100}\right)$

  $\log 2=t*\log \left(1.078\right)$

from logarithmic table we know that $\log 2=0.301$ and $\log \left(1.078\right)=0.0326$ , so

  $0.301=t*0.0326$

  $t=9.228$

here $9<t<10$

Conclusion: option I is correct.