Time to accumulate a given sum Personal Finance Problem Manuel Rios wishes to determine how long it will take an initial deposit of $$12,000$ to double.

a$.$ If Manuel earns $7\%$ annual interest on the deposit, how long will it take for him to double his money?

b$.$ How long will it take if he earns only $4\%$ annual interest?

c$.$ How long will it take if he can earn $9\%$ annual interest?

d$.$ Reviewing your findings in parts $a,b,$ and $c,$ indicate what relationship exists between the interest rate and the amount of time it will take Manuel to double his money.

a$.$ If Manuel earns $7\%$ annual interest, the amount of time to double his money is years. $($Round to two decimal places.$)$

b$.$ If Manuel earns $4\%$ annual interest, the amount of time to double his money is years. $($Round to two decimal places.$)$

c$.$ If Manuel earns $9\%$ annual interest the amount of time to double his money is years. $($Round to two decimal places.$)$

d$.$ Reviewing your findings in parts $a,b,$ and $c,$ indicate what relationship exists between the interest rate and the amount of time it will take Manuel to double his money. $($Select the best answer below.$)$

A$.$ The lower the rate of interest, the less time is required to accumulate a given future sum.

B$.$ The interest rate does not affect how long it will take to accumulate a given future value.

C$.$ The higher the rate of interest, the more time is required to accumulate a given future sum.

D$.$ The higher the rate of interest, the less time is required to accumulate a given future sum.