Question

Jackson invested $81,000 in an account paying an interest rate of 6\tfrac{1}{2}6
2
1
​
% compounded monthly. Angel invested $81,000 in an account paying an interest rate of 7\tfrac{1}{8}7
8
1
​
% compounded quarterly. After 16 years, how much more money would Angel have in his account than Jackson, to the nearest dollar?

Answer 1

Answer:22215

Step-by-step explanation: got it from delta math

Answer 2

After 16 years Angel would have amount $22942 more money in his account than Jackson.

What is compound interest?

Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

For the given situation,

Investment of Jackson, p = $81000

Rate of interest, r = 6 1/2%

⇒ $6.5\% = 0.065$

Interest is compounded monthly, so n = 12

Number of years, T = 16

Investment of Angel, p = $81000

Rate of interest, r = 7 1/8%

⇒ $7.125\% = 0.07125$

Interest is compounded quarterly, so n = 4

Number of years, T = 16

The formula of amount in compound interest is

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

Jackson's amount after 16 years,

⇒ $A=81000(1+\frac{0.065}{12} )^{(12)(16)}$

⇒ $A=81000(\frac{12.065}{12} )^{192}$

⇒ $A=81000(1.0054)^{192}$

⇒ $A=81000(2.8123)$

⇒ $A=227798.13$

Angel's amount after 16 years,

⇒ $A=81000(1+\frac{0.07125}{4} )^{(4)(16)}$

⇒ $A=81000(\frac{4.07125}{4} )^{64}$

⇒ $A=81000(1.0178)^{64}$

⇒ $A=81000(3.0955)$

⇒ $A=250739.62$

After 16 years, how much more money would Angel have in his account than Jackson is

⇒ $250739.62-227798.13$

⇒ $22941.49$ ≈ $22942$

Hence we can conclude that after 16 years Angel would have $22942 more money in his account than Jackson.

Learn more about compound interest here

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