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Kipish [7]
3 years ago
15

Greg deposited $4000 into an account with 4.6% interest, compounded semiannually. Assuming that no withdrawals are made, how muc

h will he have in the account after 7 years?
Mathematics
1 answer:
Zinaida [17]3 years ago
4 0

The amount in account after 7 years is $ 5499.445

<em><u>Solution:</u></em>

<em><u>The formula for total amount in compound interest is given as:</u></em>

A = p(1+\frac{r}{n})^{nt}

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Here given that,

A = ?

P = 4000

t = 7 years

r = 4.6 \% = \frac{4.6}{100} = 0.046

n = 2 ( since compounded semi annually)

<em><u>Substituting the values in formula, we get</u></em>

A = 4000(1+\frac{0.046}{2})^{2 \times 7}\\\\Simplify\ the\ above\ expression\\\\A = 4000(1+0.023)^{14}\\\\A = 4000(1.023)^{14}\\\\A = 4000 \times 1.37486\\\\A = 5499.445

Thus amount in account after 7 years is $ 5499.445

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