Question

Rajesh invested $30,000 into an account that compounds interest monthly at a rate of 2.16%. He has made arrangements to withdraw $300 automatically every month to pay off his 10-year student loan. Will Rajesh have enough money in the account to cover all of the required loan payments? (Round to the nearest tenth of a year.)

Answer 1

By Evaluating the Compound Interest, we come to know that Rajesh will have enough money in the account to cover all of the required loan payments.

The Principal Amount(P) = $30,000

Rate of Interest (r) = 2.16 %

Time(t) = 10 years

Number of Times it is Compounded in a year(n) = 12

Now, we have

$A =P(1+\frac{r}{100n}) ^{nt}$

Putting all the values, we evaluate the amount,

$A =30,000(1+\frac{2.16}{100*12}) ^{12*10}\\\\A = 30,000 * 1.240\\A = 37,225.84$

Hence, the Amount after Compound Interest = $37,225.87

Now, The loan amount that he pays = 300 *12*10 = $ 36,000

Yes, he will have enough money in the account to cover all of the required loan payments.

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