You have just deposited $5,000 into an account that promises to pay you an annual interest rate of 5.3 percent each year for the next 4 years. You will leave the money invested in the account and 10 years from today, you need to have $7,990 in the account. What annual interest rate must you earn over the last 6 years to accomplish this goal?

An interest rate of 4.5% needs to be earned over the last 6 years to accomplish this goal

Explanation:

Firstly, we calculate the interest value on the $5000 deposited at interest of 5.3% for 4 years

We can use the compound interest formula to know the value of the amount

A =I(1 + r)^nt

Where A is the amount which we want to calculate

I is the amount deposited = 5.3% = 5.3/100 = 0.053

n is the number of times per year in which interest is compounded = 1 (annually)

t is the number of years = 4

Plugging the values, we have ;

A = 5000(1 + 0.053)^(4)(1)

A = 5000(1.053)^4

A = $6147.29 which is approximately $6147

Now we want to know the amount of annual interest to be earned over the next 6 years

In this case our A = $7,990

I = $6147

n = 1

t = 6

r = ?

Substituting the values, we have ;

7990= 6147(1 + r)^6

divide both side by 6147

1.3 = (1+r)^6

1+ r = 1.045

r = 1.045-1

r = 0.045 which is same as 4.5%

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