Question

4. Mike and Melissa receive $20,000 in gifts from friends and relativesfor their wedding. They deposit the money into an account that pays2.75% interest compounded daily.(a) Will their money double within 10 years?(b) Will their money double within 15 years?

Answer 1

The rule of compounded interest is

`A=P(1+(r)/(n))^(nt)`

Where

A is the new amount

P is the initial amount

r is the ratio in decimal

n is t period of the time

t is the time

Let us find the values of these unknowns

They received $20,000

P = 20,000

The account pays 2.75%

r = 2.75/100 = 0.0275

The interset is compounded daily

n = 365

For (a) t = 10 years

Let us substitute these values in the rule to find A

`A=20,000(1+(0.0275)/(365))^(365(10))`

Use the calculator to find the answer

A = 26,330.34074

Let us check A is double P or not

P = 20,000

P * 2 = 2 * 20,000 = 40,000

A not equal 40,000

Their money will not double within 10 years

Change t to 15 and find the new A

`A=20,000(1+(0.0275)/(365))^(365(15))`

A = 30,211.3214

A < 40,000

Their money will not double within 15 years